TSTP Solution File: SEU039+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 2 00:06:17 EDT 2023
% Result : Theorem 52.00s 7.73s
% Output : Refutation 52.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1553
% Syntax : Number of formulae : 5142 ( 126 unt; 0 def)
% Number of atoms : 21502 (1661 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 27466 (11106 ~;14635 |; 174 &)
% (1507 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 1502 (1500 usr;1490 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-3 aty)
% Number of variables : 8767 (;8712 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f55754,plain,
$false,
inference(avatar_sat_refutation,[],[f222,f227,f232,f237,f242,f247,f252,f257,f262,f267,f272,f277,f282,f287,f292,f297,f302,f307,f312,f317,f322,f327,f332,f337,f341,f345,f349,f353,f357,f361,f375,f379,f383,f387,f391,f395,f399,f404,f408,f412,f416,f436,f442,f446,f450,f454,f478,f484,f488,f492,f496,f500,f504,f508,f538,f542,f546,f550,f554,f559,f596,f600,f604,f608,f612,f617,f635,f639,f643,f654,f658,f662,f666,f670,f680,f686,f690,f694,f720,f728,f733,f737,f742,f752,f757,f768,f776,f781,f786,f792,f798,f804,f809,f815,f820,f825,f829,f839,f848,f871,f894,f904,f913,f918,f923,f928,f932,f938,f942,f946,f950,f954,f961,f967,f968,f969,f970,f971,f1005,f1065,f1076,f1080,f1084,f1093,f1098,f1105,f1109,f1113,f1158,f1163,f1167,f1171,f1175,f1192,f1196,f1200,f1207,f1211,f1215,f1266,f1271,f1275,f1279,f1302,f1306,f1310,f1314,f1318,f1356,f1360,f1364,f1368,f1375,f1393,f1397,f1401,f1405,f1409,f1413,f1479,f1483,f1487,f1491,f1495,f1500,f1504,f1531,f1535,f1539,f1544,f1548,f1552,f1556,f1560,f1564,f1568,f1594,f1650,f1654,f1667,f1673,f1677,f1683,f1687,f1691,f1696,f1743,f1770,f1774,f1778,f1782,f1786,f1890,f1899,f1907,f1911,f1919,f1924,f1929,f1933,f1937,f1941,f1955,f1996,f2000,f2010,f2016,f2020,f2026,f2030,f2034,f2053,f2080,f2091,f2104,f2114,f2118,f2122,f2126,f2146,f2150,f2154,f2158,f2162,f2166,f2196,f2224,f2239,f2254,f2258,f2273,f2288,f2296,f2300,f2304,f2308,f2329,f2333,f2437,f2441,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2557,f2561,f2565,f2569,f2573,f2600,f2701,f2705,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2765,f2773,f2777,f2781,f2785,f2789,f2793,f2797,f2801,f2836,f2961,f2965,f2969,f2973,f2977,f2981,f3005,f3017,f3021,f3025,f3029,f3033,f3037,f3053,f3057,f3061,f3065,f3069,f3073,f3077,f3110,f3187,f3191,f3227,f3231,f3235,f3239,f3252,f3258,f3262,f3266,f3270,f3274,f3295,f3317,f3321,f3325,f3329,f3333,f3337,f3341,f3345,f3366,f3370,f3374,f3378,f3382,f3386,f3390,f3394,f3398,f3402,f3423,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3674,f3748,f3752,f3756,f3760,f3761,f3765,f3829,f3833,f3851,f3855,f3859,f3863,f3867,f3871,f3875,f3933,f4025,f4029,f4033,f4037,f4041,f4053,f4121,f4125,f4129,f4133,f4137,f4141,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4548,f4552,f4556,f4560,f4564,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4771,f4940,f4944,f4948,f4952,f4959,f4963,f5077,f5081,f5091,f5095,f5125,f5155,f5185,f5197,f5201,f5213,f5352,f5356,f5360,f5364,f5368,f5372,f5456,f5460,f5464,f5468,f5476,f5480,f5568,f5655,f5692,f5729,f5766,f5803,f5841,f5845,f5882,f5919,f5956,f5993,f6032,f6069,f6089,f6109,f6129,f6133,f6137,f6141,f6145,f6149,f6153,f6157,f6161,f6165,f6169,f6277,f6281,f6285,f6289,f6293,f6297,f6301,f6305,f6309,f6313,f6317,f6321,f6325,f6362,f6372,f6376,f6380,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6476,f6480,f6497,f6501,f6505,f6509,f6513,f6543,f6561,f6574,f6578,f6617,f6621,f6625,f6629,f6653,f6657,f6679,f6683,f6687,f6691,f6695,f6699,f6703,f6707,f6711,f6715,f6908,f6921,f6964,f6996,f7004,f7008,f7016,f7024,f7028,f7032,f7064,f7066,f7072,f7129,f7137,f7145,f7149,f7172,f7176,f7180,f7184,f7188,f7192,f7196,f7200,f7204,f7259,f7290,f7308,f7316,f7324,f7328,f7341,f7346,f7351,f7355,f7427,f7431,f7435,f7439,f7447,f7468,f7495,f7499,f7503,f7507,f7527,f7542,f7546,f7550,f7596,f7600,f7604,f7608,f7612,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7644,f7651,f7655,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7852,f7902,f7908,f7912,f7916,f7933,f7937,f7941,f7945,f7949,f7953,f7957,f7962,f8056,f8127,f8131,f8135,f8222,f8227,f8231,f8235,f8239,f8243,f8247,f8585,f8678,f8683,f8687,f8691,f8709,f8713,f8717,f8721,f8725,f8729,f8733,f8737,f8741,f8745,f8762,f8766,f8770,f8774,f8778,f8782,f8786,f8791,f8839,f9207,f9216,f9220,f9224,f9228,f9232,f9236,f9240,f9244,f9248,f9253,f9257,f9261,f9265,f9420,f9666,f9670,f9674,f9719,f9742,f9760,f9812,f9816,f9820,f9824,f9828,f9833,f9948,f9953,f9957,f9961,f9965,f9969,f9973,f9977,f10314,f10331,f10335,f10339,f10343,f10348,f10352,f10457,f10461,f10465,f10469,f10473,f10545,f10549,f10553,f10557,f10561,f10620,f10645,f10649,f10653,f10657,f10673,f10677,f10681,f10685,f10689,f10693,f10697,f10701,f10705,f10709,f10731,f10735,f10739,f10743,f10747,f10751,f10755,f10759,f10763,f10767,f10789,f10793,f10797,f10801,f10805,f10809,f11446,f11450,f11454,f11458,f11465,f11469,f11557,f11561,f11565,f11569,f11653,f11951,f11955,f11959,f11963,f11964,f11968,f11972,f11976,f11980,f11984,f11988,f11992,f11996,f12000,f12004,f12162,f12166,f12170,f12174,f12281,f12593,f12597,f12601,f12605,f12609,f12613,f12617,f12621,f12625,f12629,f12633,f12637,f12641,f12645,f12649,f12653,f12657,f12661,f12672,f12676,f12680,f13569,f13589,f13624,f13628,f13632,f13636,f13712,f13716,f13720,f13724,f13728,f13732,f13736,f13740,f13744,f13748,f13752,f13756,f13760,f13764,f13768,f13772,f13776,f13844,f13848,f13852,f13856,f14028,f14129,f14152,f14160,f14164,f14168,f14172,f14181,f14185,f14189,f14193,f14615,f14670,f14674,f14678,f14682,f14695,f14707,f14711,f14715,f14719,f14723,f14727,f14731,f14735,f14746,f14750,f14754,f14758,f14762,f14766,f14770,f14846,f15009,f15013,f15017,f15021,f15025,f15029,f15033,f15037,f15041,f15045,f15049,f15162,f15166,f15170,f15174,f15178,f15182,f15379,f15952,f15956,f15960,f15964,f15968,f15972,f15976,f15980,f15981,f16079,f16139,f16199,f16204,f16217,f16229,f16244,f16261,f16283,f16300,f16305,f16327,f16342,f16346,f16350,f16354,f16358,f16362,f16366,f16371,f16375,f16379,f16383,f16387,f16391,f16395,f16399,f16403,f16407,f16412,f16416,f16420,f16424,f16428,f16432,f16436,f16440,f16444,f16448,f16452,f16457,f16461,f16465,f16469,f16473,f16477,f16481,f16485,f16489,f16493,f16497,f16502,f16506,f16510,f16514,f16935,f17765,f17933,f17945,f18006,f18055,f18059,f18063,f18067,f18071,f18075,f18079,f18083,f18087,f18091,f18095,f18099,f18103,f18107,f18111,f18115,f18119,f18123,f18127,f18131,f18135,f18139,f18143,f18147,f18151,f18242,f18246,f18337,f18341,f18411,f18481,f18485,f18489,f18565,f18569,f18573,f20382,f20386,f20390,f20394,f20434,f20520,f20524,f20528,f20532,f20536,f20540,f20544,f20548,f20552,f20556,f20560,f20564,f20568,f20572,f20576,f20580,f20584,f20588,f20592,f20596,f20600,f20604,f20608,f20612,f20616,f20620,f20624,f20628,f20632,f20636,f20640,f20644,f20648,f20652,f20656,f21172,f22335,f23195,f23199,f23203,f23207,f23657,f23667,f23671,f23675,f23679,f23683,f23687,f23707,f23711,f23715,f23719,f23723,f23727,f23731,f23735,f23739,f23743,f23755,f23759,f23763,f23767,f23771,f23775,f23779,f23783,f23787,f23791,f23800,f23804,f23808,f24071,f25339,f25406,f25417,f25421,f25425,f25429,f25433,f25437,f25441,f25662,f25666,f25670,f25674,f25678,f25682,f25686,f25690,f25694,f25698,f25702,f25706,f25710,f25714,f25718,f25722,f25726,f25730,f25734,f25738,f25742,f26658,f27012,f27056,f27060,f27064,f27068,f27076,f27080,f27084,f27088,f27092,f27096,f27100,f27104,f27108,f27112,f27125,f27129,f27133,f27137,f27141,f27145,f27149,f27153,f27157,f27161,f27165,f27169,f27173,f27177,f27181,f27185,f27189,f27193,f27265,f27342,f27346,f27350,f27354,f27358,f27362,f27366,f27370,f27374,f27378,f27382,f27387,f27391,f27395,f27399,f27403,f27407,f27411,f27415,f27419,f27423,f27424,f27428,f27432,f27436,f27440,f27444,f27448,f28761,f29032,f29036,f29040,f29044,f29048,f29052,f29056,f29061,f29065,f29069,f29073,f29077,f29081,f29085,f29089,f29093,f29097,f29098,f29102,f29106,f29110,f29114,f29118,f29122,f29126,f29130,f29134,f29138,f29332,f29336,f29340,f29344,f29348,f29352,f29356,f29360,f29364,f29368,f29465,f29469,f29473,f29477,f29481,f29485,f29489,f29493,f29497,f29501,f29506,f29511,f29515,f29519,f29523,f29527,f29531,f29896,f31331,f32251,f33165,f33597,f33602,f33606,f33610,f33614,f33618,f33622,f33626,f33630,f33634,f33638,f33642,f33647,f33651,f33655,f33659,f33663,f33667,f33671,f33675,f33679,f33683,f33687,f33692,f33696,f33700,f33704,f33708,f33712,f33716,f33720,f33724,f33728,f33732,f33776,f33780,f33784,f33788,f33792,f33796,f33800,f33804,f33808,f33812,f33856,f33860,f33868,f33876,f33880,f33884,f33888,f33892,f33936,f33940,f33944,f33948,f33952,f33956,f33960,f33964,f33968,f33972,f34016,f34020,f35035,f38232,f39582,f39598,f39603,f39609,f39613,f39617,f39621,f39625,f39629,f39633,f39637,f39641,f39645,f39649,f39653,f39657,f39661,f39665,f39669,f39673,f39677,f39681,f39685,f39689,f39693,f39697,f39701,f39705,f39709,f39713,f39717,f39721,f39725,f39729,f39733,f39737,f39741,f39745,f39749,f39753,f39764,f39768,f39772,f39776,f39780,f39784,f39788,f39792,f39796,f39800,f39814,f39818,f39822,f39826,f39830,f39834,f39838,f39842,f39846,f39850,f39864,f39868,f39872,f39876,f39880,f39884,f39888,f39892,f39896,f39900,f40111,f40115,f40119,f40123,f40127,f40131,f40135,f40139,f40143,f40147,f40152,f40156,f43206,f46606,f47586,f47715,f47724,f47728,f47732,f47736,f47740,f47744,f47748,f47752,f47756,f47760,f47764,f47768,f47772,f47776,f47780,f47784,f47788,f47792,f47796,f47816,f47820,f47824,f48809,f48813,f48817,f48821,f48825,f48829,f48833,f48851,f48855,f48859,f48863,f48867,f48871,f48875,f48879,f48883,f48887,f48891,f48896,f48900,f48904,f48908,f48912,f48916,f48920,f48924,f48928,f48932,f48936,f48940,f48944,f48948,f48952,f48956,f48960,f48964,f48968,f48972,f48976,f48983,f48987,f48991,f48995,f48999,f49003,f49007,f49011,f49015,f49019,f49023,f49027,f49031,f49035,f49039,f49043,f49047,f49051,f49055,f49059,f49856,f51827,f55003,f55149,f55153,f55157,f55161,f55165,f55171,f55175,f55179,f55183,f55187,f55191,f55195,f55199,f55203,f55207,f55211,f55215,f55219,f55223,f55227,f55231,f55235,f55239,f55243,f55247,f55251,f55536,f55540,f55544,f55548,f55552,f55556,f55560,f55564,f55568,f55572,f55577,f55581,f55585,f55589,f55593,f55597,f55601,f55605,f55609,f55613,f55617,f55630,f55634,f55638,f55642,f55646,f55650,f55654,f55658,f55662,f55666,f55671,f55675,f55679,f55683,f55687,f55691,f55695,f55699,f55703,f55707,f55711,f55716,f55720,f55724,f55728,f55732,f55736,f55740,f55744,f55748,f55752,f55753]) ).
fof(f55753,plain,
( ~ spl22_2
| ~ spl22_1
| ~ spl22_240
| spl22_1469 ),
inference(avatar_split_clause,[],[f55712,f55668,f2448,f219,f224]) ).
fof(f224,plain,
( spl22_2
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).
fof(f219,plain,
( spl22_1
<=> relation(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).
fof(f2448,plain,
( spl22_240
<=> ! [X0,X1] :
( ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_240])]) ).
fof(f55668,plain,
( spl22_1469
<=> sP1(relation_dom_restriction(sK5,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1469])]) ).
fof(f55712,plain,
( ~ relation(sK5)
| ~ function(sK5)
| ~ spl22_240
| spl22_1469 ),
inference(resolution,[],[f55670,f2449]) ).
fof(f2449,plain,
( ! [X0,X1] :
( sP1(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_240 ),
inference(avatar_component_clause,[],[f2448]) ).
fof(f55670,plain,
( ~ sP1(relation_dom_restriction(sK5,sK3))
| spl22_1469 ),
inference(avatar_component_clause,[],[f55668]) ).
fof(f55752,plain,
( spl22_1489
| ~ spl22_236
| ~ spl22_426 ),
inference(avatar_split_clause,[],[f5895,f5880,f2331,f55750]) ).
fof(f55750,plain,
( spl22_1489
<=> ! [X41,X40,X42] :
( sP2(relation_dom(X40),X41,X42)
| apply(relation_dom_restriction(sK20,X42),sK13(relation_dom(X40),X41,X42)) = apply(sK20,sK13(relation_dom(X40),X41,X42))
| ~ sP0(X40,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1489])]) ).
fof(f2331,plain,
( spl22_236
<=> ! [X22,X23] :
( ~ in(X22,relation_dom(X23))
| ~ sP0(X23,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_236])]) ).
fof(f5880,plain,
( spl22_426
<=> ! [X41,X40,X39] :
( sP2(X39,X40,X41)
| in(sK13(X39,X40,X41),X39)
| apply(relation_dom_restriction(sK20,X41),sK13(X39,X40,X41)) = apply(sK20,sK13(X39,X40,X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_426])]) ).
fof(f5895,plain,
( ! [X40,X41,X42] :
( sP2(relation_dom(X40),X41,X42)
| apply(relation_dom_restriction(sK20,X42),sK13(relation_dom(X40),X41,X42)) = apply(sK20,sK13(relation_dom(X40),X41,X42))
| ~ sP0(X40,sK15) )
| ~ spl22_236
| ~ spl22_426 ),
inference(resolution,[],[f5881,f2332]) ).
fof(f2332,plain,
( ! [X22,X23] :
( ~ in(X22,relation_dom(X23))
| ~ sP0(X23,sK15) )
| ~ spl22_236 ),
inference(avatar_component_clause,[],[f2331]) ).
fof(f5881,plain,
( ! [X40,X41,X39] :
( in(sK13(X39,X40,X41),X39)
| sP2(X39,X40,X41)
| apply(relation_dom_restriction(sK20,X41),sK13(X39,X40,X41)) = apply(sK20,sK13(X39,X40,X41)) )
| ~ spl22_426 ),
inference(avatar_component_clause,[],[f5880]) ).
fof(f55748,plain,
( spl22_1488
| ~ spl22_45
| ~ spl22_426 ),
inference(avatar_split_clause,[],[f5888,f5880,f448,f55746]) ).
fof(f55746,plain,
( spl22_1488
<=> ! [X13,X14,X15] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(sK20,X15),sK13(X13,X14,X15)) = apply(sK20,sK13(X13,X14,X15))
| ~ in(X13,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1488])]) ).
fof(f448,plain,
( spl22_45
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_45])]) ).
fof(f5888,plain,
( ! [X14,X15,X13] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(sK20,X15),sK13(X13,X14,X15)) = apply(sK20,sK13(X13,X14,X15))
| ~ in(X13,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_426 ),
inference(resolution,[],[f5881,f449]) ).
fof(f449,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl22_45 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f55744,plain,
( spl22_1487
| ~ spl22_46
| ~ spl22_426 ),
inference(avatar_split_clause,[],[f5887,f5880,f452,f55742]) ).
fof(f55742,plain,
( spl22_1487
<=> ! [X11,X12,X10] :
( sP2(X10,X11,X12)
| apply(relation_dom_restriction(sK20,X12),sK13(X10,X11,X12)) = apply(sK20,sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1487])]) ).
fof(f452,plain,
( spl22_46
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_46])]) ).
fof(f5887,plain,
( ! [X10,X11,X12] :
( sP2(X10,X11,X12)
| apply(relation_dom_restriction(sK20,X12),sK13(X10,X11,X12)) = apply(sK20,sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X10) )
| ~ spl22_46
| ~ spl22_426 ),
inference(resolution,[],[f5881,f453]) ).
fof(f453,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f55740,plain,
( spl22_1486
| ~ spl22_236
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f5858,f5843,f2331,f55738]) ).
fof(f55738,plain,
( spl22_1486
<=> ! [X41,X40,X42] :
( sP2(relation_dom(X40),X41,X42)
| apply(relation_dom_restriction(sK19,X42),sK13(relation_dom(X40),X41,X42)) = apply(sK19,sK13(relation_dom(X40),X41,X42))
| ~ sP0(X40,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1486])]) ).
fof(f5843,plain,
( spl22_425
<=> ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| in(sK13(X36,X37,X38),X36)
| apply(relation_dom_restriction(sK19,X38),sK13(X36,X37,X38)) = apply(sK19,sK13(X36,X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_425])]) ).
fof(f5858,plain,
( ! [X40,X41,X42] :
( sP2(relation_dom(X40),X41,X42)
| apply(relation_dom_restriction(sK19,X42),sK13(relation_dom(X40),X41,X42)) = apply(sK19,sK13(relation_dom(X40),X41,X42))
| ~ sP0(X40,sK15) )
| ~ spl22_236
| ~ spl22_425 ),
inference(resolution,[],[f5844,f2332]) ).
fof(f5844,plain,
( ! [X38,X36,X37] :
( in(sK13(X36,X37,X38),X36)
| sP2(X36,X37,X38)
| apply(relation_dom_restriction(sK19,X38),sK13(X36,X37,X38)) = apply(sK19,sK13(X36,X37,X38)) )
| ~ spl22_425 ),
inference(avatar_component_clause,[],[f5843]) ).
fof(f55736,plain,
( spl22_1485
| ~ spl22_45
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f5851,f5843,f448,f55734]) ).
fof(f55734,plain,
( spl22_1485
<=> ! [X13,X14,X15] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(sK19,X15),sK13(X13,X14,X15)) = apply(sK19,sK13(X13,X14,X15))
| ~ in(X13,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1485])]) ).
fof(f5851,plain,
( ! [X14,X15,X13] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(sK19,X15),sK13(X13,X14,X15)) = apply(sK19,sK13(X13,X14,X15))
| ~ in(X13,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_425 ),
inference(resolution,[],[f5844,f449]) ).
fof(f55732,plain,
( spl22_1484
| ~ spl22_46
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f5850,f5843,f452,f55730]) ).
fof(f55730,plain,
( spl22_1484
<=> ! [X11,X12,X10] :
( sP2(X10,X11,X12)
| apply(relation_dom_restriction(sK19,X12),sK13(X10,X11,X12)) = apply(sK19,sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1484])]) ).
fof(f5850,plain,
( ! [X10,X11,X12] :
( sP2(X10,X11,X12)
| apply(relation_dom_restriction(sK19,X12),sK13(X10,X11,X12)) = apply(sK19,sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X10) )
| ~ spl22_46
| ~ spl22_425 ),
inference(resolution,[],[f5844,f453]) ).
fof(f55728,plain,
( spl22_1483
| ~ spl22_236
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f5816,f5801,f2331,f55726]) ).
fof(f55726,plain,
( spl22_1483
<=> ! [X41,X43,X42] :
( apply(sK15,sK13(X41,X42,relation_dom(X43))) = apply(relation_dom_restriction(sK15,X42),sK13(X41,X42,relation_dom(X43)))
| sP2(X41,X42,relation_dom(X43))
| ~ sP0(X43,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1483])]) ).
fof(f5801,plain,
( spl22_423
<=> ! [X20,X18,X19] :
( apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X19),sK13(X18,X19,X20))
| in(sK13(X18,X19,X20),X20)
| sP2(X18,X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_423])]) ).
fof(f5816,plain,
( ! [X41,X42,X43] :
( apply(sK15,sK13(X41,X42,relation_dom(X43))) = apply(relation_dom_restriction(sK15,X42),sK13(X41,X42,relation_dom(X43)))
| sP2(X41,X42,relation_dom(X43))
| ~ sP0(X43,sK15) )
| ~ spl22_236
| ~ spl22_423 ),
inference(resolution,[],[f5802,f2332]) ).
fof(f5802,plain,
( ! [X18,X19,X20] :
( in(sK13(X18,X19,X20),X20)
| apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X19),sK13(X18,X19,X20))
| sP2(X18,X19,X20) )
| ~ spl22_423 ),
inference(avatar_component_clause,[],[f5801]) ).
fof(f55724,plain,
( spl22_1482
| ~ spl22_45
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f5809,f5801,f448,f55722]) ).
fof(f55722,plain,
( spl22_1482
<=> ! [X16,X14,X15] :
( apply(sK15,sK13(X14,X15,X16)) = apply(relation_dom_restriction(sK15,X15),sK13(X14,X15,X16))
| sP2(X14,X15,X16)
| ~ in(X16,sK13(X14,X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1482])]) ).
fof(f5809,plain,
( ! [X16,X14,X15] :
( apply(sK15,sK13(X14,X15,X16)) = apply(relation_dom_restriction(sK15,X15),sK13(X14,X15,X16))
| sP2(X14,X15,X16)
| ~ in(X16,sK13(X14,X15,X16)) )
| ~ spl22_45
| ~ spl22_423 ),
inference(resolution,[],[f5802,f449]) ).
fof(f55720,plain,
( spl22_1481
| ~ spl22_46
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f5808,f5801,f452,f55718]) ).
fof(f55718,plain,
( spl22_1481
<=> ! [X13,X12,X11] :
( apply(sK15,sK13(X11,X12,X13)) = apply(relation_dom_restriction(sK15,X12),sK13(X11,X12,X13))
| sP2(X11,X12,X13)
| element(sK13(X11,X12,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1481])]) ).
fof(f5808,plain,
( ! [X11,X12,X13] :
( apply(sK15,sK13(X11,X12,X13)) = apply(relation_dom_restriction(sK15,X12),sK13(X11,X12,X13))
| sP2(X11,X12,X13)
| element(sK13(X11,X12,X13),X13) )
| ~ spl22_46
| ~ spl22_423 ),
inference(resolution,[],[f5802,f453]) ).
fof(f55716,plain,
( spl22_1480
| ~ spl22_236
| ~ spl22_422 ),
inference(avatar_split_clause,[],[f5779,f5764,f2331,f55714]) ).
fof(f55714,plain,
( spl22_1480
<=> ! [X41,X43,X42] :
( sP2(X41,X42,relation_dom(X43))
| apply(sK20,sK13(X41,X42,relation_dom(X43))) = apply(relation_dom_restriction(sK20,X42),sK13(X41,X42,relation_dom(X43)))
| ~ sP0(X43,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1480])]) ).
fof(f5764,plain,
( spl22_422
<=> ! [X41,X40,X39] :
( sP2(X39,X40,X41)
| in(sK13(X39,X40,X41),X41)
| apply(sK20,sK13(X39,X40,X41)) = apply(relation_dom_restriction(sK20,X40),sK13(X39,X40,X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_422])]) ).
fof(f5779,plain,
( ! [X41,X42,X43] :
( sP2(X41,X42,relation_dom(X43))
| apply(sK20,sK13(X41,X42,relation_dom(X43))) = apply(relation_dom_restriction(sK20,X42),sK13(X41,X42,relation_dom(X43)))
| ~ sP0(X43,sK15) )
| ~ spl22_236
| ~ spl22_422 ),
inference(resolution,[],[f5765,f2332]) ).
fof(f5765,plain,
( ! [X40,X41,X39] :
( in(sK13(X39,X40,X41),X41)
| sP2(X39,X40,X41)
| apply(sK20,sK13(X39,X40,X41)) = apply(relation_dom_restriction(sK20,X40),sK13(X39,X40,X41)) )
| ~ spl22_422 ),
inference(avatar_component_clause,[],[f5764]) ).
fof(f55711,plain,
( spl22_1479
| ~ spl22_45
| ~ spl22_422 ),
inference(avatar_split_clause,[],[f5772,f5764,f448,f55709]) ).
fof(f55709,plain,
( spl22_1479
<=> ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(sK20,sK13(X14,X15,X16)) = apply(relation_dom_restriction(sK20,X15),sK13(X14,X15,X16))
| ~ in(X16,sK13(X14,X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1479])]) ).
fof(f5772,plain,
( ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(sK20,sK13(X14,X15,X16)) = apply(relation_dom_restriction(sK20,X15),sK13(X14,X15,X16))
| ~ in(X16,sK13(X14,X15,X16)) )
| ~ spl22_45
| ~ spl22_422 ),
inference(resolution,[],[f5765,f449]) ).
fof(f55707,plain,
( spl22_1478
| ~ spl22_46
| ~ spl22_422 ),
inference(avatar_split_clause,[],[f5771,f5764,f452,f55705]) ).
fof(f55705,plain,
( spl22_1478
<=> ! [X13,X12,X11] :
( sP2(X11,X12,X13)
| apply(sK20,sK13(X11,X12,X13)) = apply(relation_dom_restriction(sK20,X12),sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1478])]) ).
fof(f5771,plain,
( ! [X11,X12,X13] :
( sP2(X11,X12,X13)
| apply(sK20,sK13(X11,X12,X13)) = apply(relation_dom_restriction(sK20,X12),sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X13) )
| ~ spl22_46
| ~ spl22_422 ),
inference(resolution,[],[f5765,f453]) ).
fof(f55703,plain,
( spl22_1477
| ~ spl22_236
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5742,f5727,f2331,f55701]) ).
fof(f55701,plain,
( spl22_1477
<=> ! [X41,X43,X42] :
( sP2(X41,X42,relation_dom(X43))
| apply(sK19,sK13(X41,X42,relation_dom(X43))) = apply(relation_dom_restriction(sK19,X42),sK13(X41,X42,relation_dom(X43)))
| ~ sP0(X43,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1477])]) ).
fof(f5727,plain,
( spl22_421
<=> ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| in(sK13(X36,X37,X38),X38)
| apply(sK19,sK13(X36,X37,X38)) = apply(relation_dom_restriction(sK19,X37),sK13(X36,X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_421])]) ).
fof(f5742,plain,
( ! [X41,X42,X43] :
( sP2(X41,X42,relation_dom(X43))
| apply(sK19,sK13(X41,X42,relation_dom(X43))) = apply(relation_dom_restriction(sK19,X42),sK13(X41,X42,relation_dom(X43)))
| ~ sP0(X43,sK15) )
| ~ spl22_236
| ~ spl22_421 ),
inference(resolution,[],[f5728,f2332]) ).
fof(f5728,plain,
( ! [X38,X36,X37] :
( in(sK13(X36,X37,X38),X38)
| sP2(X36,X37,X38)
| apply(sK19,sK13(X36,X37,X38)) = apply(relation_dom_restriction(sK19,X37),sK13(X36,X37,X38)) )
| ~ spl22_421 ),
inference(avatar_component_clause,[],[f5727]) ).
fof(f55699,plain,
( spl22_1476
| ~ spl22_45
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5735,f5727,f448,f55697]) ).
fof(f55697,plain,
( spl22_1476
<=> ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(sK19,sK13(X14,X15,X16)) = apply(relation_dom_restriction(sK19,X15),sK13(X14,X15,X16))
| ~ in(X16,sK13(X14,X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1476])]) ).
fof(f5735,plain,
( ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(sK19,sK13(X14,X15,X16)) = apply(relation_dom_restriction(sK19,X15),sK13(X14,X15,X16))
| ~ in(X16,sK13(X14,X15,X16)) )
| ~ spl22_45
| ~ spl22_421 ),
inference(resolution,[],[f5728,f449]) ).
fof(f55695,plain,
( spl22_1475
| ~ spl22_46
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5734,f5727,f452,f55693]) ).
fof(f55693,plain,
( spl22_1475
<=> ! [X13,X12,X11] :
( sP2(X11,X12,X13)
| apply(sK19,sK13(X11,X12,X13)) = apply(relation_dom_restriction(sK19,X12),sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1475])]) ).
fof(f5734,plain,
( ! [X11,X12,X13] :
( sP2(X11,X12,X13)
| apply(sK19,sK13(X11,X12,X13)) = apply(relation_dom_restriction(sK19,X12),sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X13) )
| ~ spl22_46
| ~ spl22_421 ),
inference(resolution,[],[f5728,f453]) ).
fof(f55691,plain,
( spl22_1474
| ~ spl22_319
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5724,f5690,f3343,f55689]) ).
fof(f55689,plain,
( spl22_1474
<=> ! [X2,X3] :
( apply(relation_dom_restriction(sK15,X2),sK13(X2,X3,X2)) = apply(sK15,sK13(X2,X3,X2))
| sP2(X2,X3,X2)
| ~ in(sK13(X2,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1474])]) ).
fof(f3343,plain,
( spl22_319
<=> ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(sK13(X0,X1,X0),X0)
| ~ in(sK13(X0,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_319])]) ).
fof(f5690,plain,
( spl22_420
<=> ! [X20,X18,X19] :
( apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| in(sK13(X18,X19,X20),X19)
| sP2(X18,X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_420])]) ).
fof(f5724,plain,
( ! [X2,X3] :
( apply(relation_dom_restriction(sK15,X2),sK13(X2,X3,X2)) = apply(sK15,sK13(X2,X3,X2))
| sP2(X2,X3,X2)
| ~ in(sK13(X2,X3,X2),X2) )
| ~ spl22_319
| ~ spl22_420 ),
inference(duplicate_literal_removal,[],[f5694]) ).
fof(f5694,plain,
( ! [X2,X3] :
( apply(relation_dom_restriction(sK15,X2),sK13(X2,X3,X2)) = apply(sK15,sK13(X2,X3,X2))
| sP2(X2,X3,X2)
| ~ in(sK13(X2,X3,X2),X2)
| sP2(X2,X3,X2) )
| ~ spl22_319
| ~ spl22_420 ),
inference(resolution,[],[f5691,f3344]) ).
fof(f3344,plain,
( ! [X0,X1] :
( ~ in(sK13(X0,X1,X0),X1)
| ~ in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl22_319 ),
inference(avatar_component_clause,[],[f3343]) ).
fof(f5691,plain,
( ! [X18,X19,X20] :
( in(sK13(X18,X19,X20),X19)
| apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| sP2(X18,X19,X20) )
| ~ spl22_420 ),
inference(avatar_component_clause,[],[f5690]) ).
fof(f55687,plain,
( spl22_1473
| ~ spl22_236
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5705,f5690,f2331,f55685]) ).
fof(f55685,plain,
( spl22_1473
<=> ! [X41,X43,X42] :
( apply(relation_dom_restriction(sK15,X41),sK13(X42,relation_dom(X43),X41)) = apply(sK15,sK13(X42,relation_dom(X43),X41))
| sP2(X42,relation_dom(X43),X41)
| ~ sP0(X43,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1473])]) ).
fof(f5705,plain,
( ! [X41,X42,X43] :
( apply(relation_dom_restriction(sK15,X41),sK13(X42,relation_dom(X43),X41)) = apply(sK15,sK13(X42,relation_dom(X43),X41))
| sP2(X42,relation_dom(X43),X41)
| ~ sP0(X43,sK15) )
| ~ spl22_236
| ~ spl22_420 ),
inference(resolution,[],[f5691,f2332]) ).
fof(f55683,plain,
( spl22_1472
| ~ spl22_45
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5698,f5690,f448,f55681]) ).
fof(f55681,plain,
( spl22_1472
<=> ! [X16,X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK13(X15,X16,X14)) = apply(sK15,sK13(X15,X16,X14))
| sP2(X15,X16,X14)
| ~ in(X16,sK13(X15,X16,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1472])]) ).
fof(f5698,plain,
( ! [X16,X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK13(X15,X16,X14)) = apply(sK15,sK13(X15,X16,X14))
| sP2(X15,X16,X14)
| ~ in(X16,sK13(X15,X16,X14)) )
| ~ spl22_45
| ~ spl22_420 ),
inference(resolution,[],[f5691,f449]) ).
fof(f55679,plain,
( spl22_1471
| ~ spl22_46
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5697,f5690,f452,f55677]) ).
fof(f55677,plain,
( spl22_1471
<=> ! [X13,X12,X11] :
( apply(relation_dom_restriction(sK15,X11),sK13(X12,X13,X11)) = apply(sK15,sK13(X12,X13,X11))
| sP2(X12,X13,X11)
| element(sK13(X12,X13,X11),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1471])]) ).
fof(f5697,plain,
( ! [X11,X12,X13] :
( apply(relation_dom_restriction(sK15,X11),sK13(X12,X13,X11)) = apply(sK15,sK13(X12,X13,X11))
| sP2(X12,X13,X11)
| element(sK13(X12,X13,X11),X13) )
| ~ spl22_46
| ~ spl22_420 ),
inference(resolution,[],[f5691,f453]) ).
fof(f55675,plain,
( spl22_1470
| ~ spl22_236
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5668,f5653,f2331,f55673]) ).
fof(f55673,plain,
( spl22_1470
<=> ! [X41,X43,X42] :
( sP2(X41,relation_dom(X42),X43)
| apply(relation_dom_restriction(sK20,X43),sK13(X41,relation_dom(X42),X43)) = apply(sK20,sK13(X41,relation_dom(X42),X43))
| ~ sP0(X42,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1470])]) ).
fof(f5653,plain,
( spl22_419
<=> ! [X41,X40,X39] :
( sP2(X39,X40,X41)
| in(sK13(X39,X40,X41),X40)
| apply(relation_dom_restriction(sK20,X41),sK13(X39,X40,X41)) = apply(sK20,sK13(X39,X40,X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_419])]) ).
fof(f5668,plain,
( ! [X41,X42,X43] :
( sP2(X41,relation_dom(X42),X43)
| apply(relation_dom_restriction(sK20,X43),sK13(X41,relation_dom(X42),X43)) = apply(sK20,sK13(X41,relation_dom(X42),X43))
| ~ sP0(X42,sK15) )
| ~ spl22_236
| ~ spl22_419 ),
inference(resolution,[],[f5654,f2332]) ).
fof(f5654,plain,
( ! [X40,X41,X39] :
( in(sK13(X39,X40,X41),X40)
| sP2(X39,X40,X41)
| apply(relation_dom_restriction(sK20,X41),sK13(X39,X40,X41)) = apply(sK20,sK13(X39,X40,X41)) )
| ~ spl22_419 ),
inference(avatar_component_clause,[],[f5653]) ).
fof(f55671,plain,
( ~ spl22_1469
| spl22_5
| ~ spl22_125
| ~ spl22_501 ),
inference(avatar_split_clause,[],[f16029,f6994,f1107,f239,f55668]) ).
fof(f239,plain,
( spl22_5
<=> in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).
fof(f1107,plain,
( spl22_125
<=> ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_125])]) ).
fof(f6994,plain,
( spl22_501
<=> ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_501])]) ).
fof(f16029,plain,
( in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
| ~ sP1(relation_dom_restriction(sK5,sK3))
| ~ spl22_125
| ~ spl22_501 ),
inference(resolution,[],[f6995,f1108]) ).
fof(f1108,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_125 ),
inference(avatar_component_clause,[],[f1107]) ).
fof(f6995,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),X0)
| in(apply(sK5,sK4),X0) )
| ~ spl22_501 ),
inference(avatar_component_clause,[],[f6994]) ).
fof(f55666,plain,
( spl22_1468
| ~ spl22_45
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5661,f5653,f448,f55664]) ).
fof(f55664,plain,
( spl22_1468
<=> ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(relation_dom_restriction(sK20,X16),sK13(X14,X15,X16)) = apply(sK20,sK13(X14,X15,X16))
| ~ in(X15,sK13(X14,X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1468])]) ).
fof(f5661,plain,
( ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(relation_dom_restriction(sK20,X16),sK13(X14,X15,X16)) = apply(sK20,sK13(X14,X15,X16))
| ~ in(X15,sK13(X14,X15,X16)) )
| ~ spl22_45
| ~ spl22_419 ),
inference(resolution,[],[f5654,f449]) ).
fof(f55662,plain,
( spl22_1467
| ~ spl22_46
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5660,f5653,f452,f55660]) ).
fof(f55660,plain,
( spl22_1467
<=> ! [X13,X12,X11] :
( sP2(X11,X12,X13)
| apply(relation_dom_restriction(sK20,X13),sK13(X11,X12,X13)) = apply(sK20,sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1467])]) ).
fof(f5660,plain,
( ! [X11,X12,X13] :
( sP2(X11,X12,X13)
| apply(relation_dom_restriction(sK20,X13),sK13(X11,X12,X13)) = apply(sK20,sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X12) )
| ~ spl22_46
| ~ spl22_419 ),
inference(resolution,[],[f5654,f453]) ).
fof(f55658,plain,
( spl22_1466
| ~ spl22_236
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5581,f5566,f2331,f55656]) ).
fof(f55656,plain,
( spl22_1466
<=> ! [X41,X43,X42] :
( sP2(X41,relation_dom(X42),X43)
| apply(relation_dom_restriction(sK19,X43),sK13(X41,relation_dom(X42),X43)) = apply(sK19,sK13(X41,relation_dom(X42),X43))
| ~ sP0(X42,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1466])]) ).
fof(f5566,plain,
( spl22_418
<=> ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| in(sK13(X36,X37,X38),X37)
| apply(relation_dom_restriction(sK19,X38),sK13(X36,X37,X38)) = apply(sK19,sK13(X36,X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_418])]) ).
fof(f5581,plain,
( ! [X41,X42,X43] :
( sP2(X41,relation_dom(X42),X43)
| apply(relation_dom_restriction(sK19,X43),sK13(X41,relation_dom(X42),X43)) = apply(sK19,sK13(X41,relation_dom(X42),X43))
| ~ sP0(X42,sK15) )
| ~ spl22_236
| ~ spl22_418 ),
inference(resolution,[],[f5567,f2332]) ).
fof(f5567,plain,
( ! [X38,X36,X37] :
( in(sK13(X36,X37,X38),X37)
| sP2(X36,X37,X38)
| apply(relation_dom_restriction(sK19,X38),sK13(X36,X37,X38)) = apply(sK19,sK13(X36,X37,X38)) )
| ~ spl22_418 ),
inference(avatar_component_clause,[],[f5566]) ).
fof(f55654,plain,
( spl22_1465
| ~ spl22_45
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5574,f5566,f448,f55652]) ).
fof(f55652,plain,
( spl22_1465
<=> ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(relation_dom_restriction(sK19,X16),sK13(X14,X15,X16)) = apply(sK19,sK13(X14,X15,X16))
| ~ in(X15,sK13(X14,X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1465])]) ).
fof(f5574,plain,
( ! [X16,X14,X15] :
( sP2(X14,X15,X16)
| apply(relation_dom_restriction(sK19,X16),sK13(X14,X15,X16)) = apply(sK19,sK13(X14,X15,X16))
| ~ in(X15,sK13(X14,X15,X16)) )
| ~ spl22_45
| ~ spl22_418 ),
inference(resolution,[],[f5567,f449]) ).
fof(f55650,plain,
( spl22_1464
| ~ spl22_46
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5573,f5566,f452,f55648]) ).
fof(f55648,plain,
( spl22_1464
<=> ! [X13,X12,X11] :
( sP2(X11,X12,X13)
| apply(relation_dom_restriction(sK19,X13),sK13(X11,X12,X13)) = apply(sK19,sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1464])]) ).
fof(f5573,plain,
( ! [X11,X12,X13] :
( sP2(X11,X12,X13)
| apply(relation_dom_restriction(sK19,X13),sK13(X11,X12,X13)) = apply(sK19,sK13(X11,X12,X13))
| element(sK13(X11,X12,X13),X12) )
| ~ spl22_46
| ~ spl22_418 ),
inference(resolution,[],[f5567,f453]) ).
fof(f55646,plain,
( spl22_1463
| ~ spl22_131
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5172,f5153,f1173,f55644]) ).
fof(f55644,plain,
( spl22_1463
<=> ! [X41,X42] :
( sP0(X41,sK10(powerset(X42)))
| apply(relation_dom_restriction(sK15,relation_dom(X41)),sK8(X41,sK10(powerset(X42)))) = apply(sK15,sK8(X41,sK10(powerset(X42))))
| ~ empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1463])]) ).
fof(f1173,plain,
( spl22_131
<=> ! [X6,X5] :
( ~ empty(X5)
| ~ in(X6,sK10(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_131])]) ).
fof(f5153,plain,
( spl22_401
<=> ! [X14,X15] :
( apply(relation_dom_restriction(sK15,relation_dom(X14)),sK8(X14,X15)) = apply(sK15,sK8(X14,X15))
| sP0(X14,X15)
| in(sK7(X14,X15),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_401])]) ).
fof(f5172,plain,
( ! [X41,X42] :
( sP0(X41,sK10(powerset(X42)))
| apply(relation_dom_restriction(sK15,relation_dom(X41)),sK8(X41,sK10(powerset(X42)))) = apply(sK15,sK8(X41,sK10(powerset(X42))))
| ~ empty(X42) )
| ~ spl22_131
| ~ spl22_401 ),
inference(resolution,[],[f5154,f1174]) ).
fof(f1174,plain,
( ! [X6,X5] :
( ~ in(X6,sK10(powerset(X5)))
| ~ empty(X5) )
| ~ spl22_131 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f5154,plain,
( ! [X14,X15] :
( in(sK7(X14,X15),X15)
| sP0(X14,X15)
| apply(relation_dom_restriction(sK15,relation_dom(X14)),sK8(X14,X15)) = apply(sK15,sK8(X14,X15)) )
| ~ spl22_401 ),
inference(avatar_component_clause,[],[f5153]) ).
fof(f55642,plain,
( spl22_1462
| ~ spl22_250
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5164,f5153,f2571,f55640]) ).
fof(f55640,plain,
( spl22_1462
<=> ! [X22,X20,X21] :
( sP0(X20,relation_dom(X21))
| apply(relation_dom_restriction(sK15,relation_dom(X20)),sK8(X20,relation_dom(X21))) = apply(sK15,sK8(X20,relation_dom(X21)))
| ~ sP0(X21,X22)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1462])]) ).
fof(f2571,plain,
( spl22_250
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_250])]) ).
fof(f5164,plain,
( ! [X21,X22,X20] :
( sP0(X20,relation_dom(X21))
| apply(relation_dom_restriction(sK15,relation_dom(X20)),sK8(X20,relation_dom(X21))) = apply(sK15,sK8(X20,relation_dom(X21)))
| ~ sP0(X21,X22)
| ~ empty(X22) )
| ~ spl22_250
| ~ spl22_401 ),
inference(resolution,[],[f5154,f2572]) ).
fof(f2572,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_250 ),
inference(avatar_component_clause,[],[f2571]) ).
fof(f55638,plain,
( spl22_1461
| ~ spl22_131
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5142,f5123,f1173,f55636]) ).
fof(f55636,plain,
( spl22_1461
<=> ! [X41,X42] :
( sP0(X41,sK10(powerset(X42)))
| apply(relation_dom_restriction(sK20,relation_dom(X41)),sK8(X41,sK10(powerset(X42)))) = apply(sK20,sK8(X41,sK10(powerset(X42))))
| ~ empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1461])]) ).
fof(f5123,plain,
( spl22_400
<=> ! [X29,X28] :
( apply(relation_dom_restriction(sK20,relation_dom(X28)),sK8(X28,X29)) = apply(sK20,sK8(X28,X29))
| sP0(X28,X29)
| in(sK7(X28,X29),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_400])]) ).
fof(f5142,plain,
( ! [X41,X42] :
( sP0(X41,sK10(powerset(X42)))
| apply(relation_dom_restriction(sK20,relation_dom(X41)),sK8(X41,sK10(powerset(X42)))) = apply(sK20,sK8(X41,sK10(powerset(X42))))
| ~ empty(X42) )
| ~ spl22_131
| ~ spl22_400 ),
inference(resolution,[],[f5124,f1174]) ).
fof(f5124,plain,
( ! [X28,X29] :
( in(sK7(X28,X29),X29)
| sP0(X28,X29)
| apply(relation_dom_restriction(sK20,relation_dom(X28)),sK8(X28,X29)) = apply(sK20,sK8(X28,X29)) )
| ~ spl22_400 ),
inference(avatar_component_clause,[],[f5123]) ).
fof(f55634,plain,
( spl22_1460
| ~ spl22_250
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5134,f5123,f2571,f55632]) ).
fof(f55632,plain,
( spl22_1460
<=> ! [X22,X20,X21] :
( sP0(X20,relation_dom(X21))
| apply(relation_dom_restriction(sK20,relation_dom(X20)),sK8(X20,relation_dom(X21))) = apply(sK20,sK8(X20,relation_dom(X21)))
| ~ sP0(X21,X22)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1460])]) ).
fof(f5134,plain,
( ! [X21,X22,X20] :
( sP0(X20,relation_dom(X21))
| apply(relation_dom_restriction(sK20,relation_dom(X20)),sK8(X20,relation_dom(X21))) = apply(sK20,sK8(X20,relation_dom(X21)))
| ~ sP0(X21,X22)
| ~ empty(X22) )
| ~ spl22_250
| ~ spl22_400 ),
inference(resolution,[],[f5124,f2572]) ).
fof(f55630,plain,
( spl22_1459
| ~ spl22_131
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5112,f5093,f1173,f55628]) ).
fof(f55628,plain,
( spl22_1459
<=> ! [X41,X42] :
( sP0(X41,sK10(powerset(X42)))
| apply(relation_dom_restriction(sK19,relation_dom(X41)),sK8(X41,sK10(powerset(X42)))) = apply(sK19,sK8(X41,sK10(powerset(X42))))
| ~ empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1459])]) ).
fof(f5093,plain,
( spl22_399
<=> ! [X27,X26] :
( apply(relation_dom_restriction(sK19,relation_dom(X26)),sK8(X26,X27)) = apply(sK19,sK8(X26,X27))
| sP0(X26,X27)
| in(sK7(X26,X27),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_399])]) ).
fof(f5112,plain,
( ! [X41,X42] :
( sP0(X41,sK10(powerset(X42)))
| apply(relation_dom_restriction(sK19,relation_dom(X41)),sK8(X41,sK10(powerset(X42)))) = apply(sK19,sK8(X41,sK10(powerset(X42))))
| ~ empty(X42) )
| ~ spl22_131
| ~ spl22_399 ),
inference(resolution,[],[f5094,f1174]) ).
fof(f5094,plain,
( ! [X26,X27] :
( in(sK7(X26,X27),X27)
| sP0(X26,X27)
| apply(relation_dom_restriction(sK19,relation_dom(X26)),sK8(X26,X27)) = apply(sK19,sK8(X26,X27)) )
| ~ spl22_399 ),
inference(avatar_component_clause,[],[f5093]) ).
fof(f55617,plain,
( spl22_1458
| ~ spl22_250
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5104,f5093,f2571,f55615]) ).
fof(f55615,plain,
( spl22_1458
<=> ! [X22,X20,X21] :
( sP0(X20,relation_dom(X21))
| apply(relation_dom_restriction(sK19,relation_dom(X20)),sK8(X20,relation_dom(X21))) = apply(sK19,sK8(X20,relation_dom(X21)))
| ~ sP0(X21,X22)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1458])]) ).
fof(f5104,plain,
( ! [X21,X22,X20] :
( sP0(X20,relation_dom(X21))
| apply(relation_dom_restriction(sK19,relation_dom(X20)),sK8(X20,relation_dom(X21))) = apply(sK19,sK8(X20,relation_dom(X21)))
| ~ sP0(X21,X22)
| ~ empty(X22) )
| ~ spl22_250
| ~ spl22_399 ),
inference(resolution,[],[f5094,f2572]) ).
fof(f55613,plain,
( spl22_1457
| ~ spl22_52
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4930,f4594,f498,f55611]) ).
fof(f55611,plain,
( spl22_1457
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,sK10(powerset(powerset(X10)))),X8)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1457])]) ).
fof(f498,plain,
( spl22_52
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_52])]) ).
fof(f4594,plain,
( spl22_388
<=> ! [X20,X21,X19] :
( element(sK13(X19,X20,sK10(powerset(X21))),X19)
| sP2(X19,X20,sK10(powerset(X21)))
| element(sK13(X19,X20,sK10(powerset(X21))),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_388])]) ).
fof(f4930,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK10(powerset(powerset(X10)))),X8)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) )
| ~ spl22_52
| ~ spl22_388 ),
inference(resolution,[],[f4595,f499]) ).
fof(f499,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl22_52 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f4595,plain,
( ! [X21,X19,X20] :
( element(sK13(X19,X20,sK10(powerset(X21))),X21)
| element(sK13(X19,X20,sK10(powerset(X21))),X19)
| sP2(X19,X20,sK10(powerset(X21))) )
| ~ spl22_388 ),
inference(avatar_component_clause,[],[f4594]) ).
fof(f55609,plain,
( spl22_1456
| ~ spl22_52
| ~ spl22_386 ),
inference(avatar_split_clause,[],[f4879,f4586,f498,f55607]) ).
fof(f55607,plain,
( spl22_1456
<=> ! [X9,X8,X10] :
( element(sK13(sK10(powerset(powerset(X8))),X9,X10),X10)
| sP2(sK10(powerset(powerset(X8))),X9,X10)
| subset(sK13(sK10(powerset(powerset(X8))),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1456])]) ).
fof(f4586,plain,
( spl22_386
<=> ! [X20,X18,X19] :
( element(sK13(sK10(powerset(X18)),X19,X20),X20)
| sP2(sK10(powerset(X18)),X19,X20)
| element(sK13(sK10(powerset(X18)),X19,X20),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_386])]) ).
fof(f4879,plain,
( ! [X10,X8,X9] :
( element(sK13(sK10(powerset(powerset(X8))),X9,X10),X10)
| sP2(sK10(powerset(powerset(X8))),X9,X10)
| subset(sK13(sK10(powerset(powerset(X8))),X9,X10),X8) )
| ~ spl22_52
| ~ spl22_386 ),
inference(resolution,[],[f4587,f499]) ).
fof(f4587,plain,
( ! [X18,X19,X20] :
( element(sK13(sK10(powerset(X18)),X19,X20),X20)
| element(sK13(sK10(powerset(X18)),X19,X20),X18)
| sP2(sK10(powerset(X18)),X19,X20) )
| ~ spl22_386 ),
inference(avatar_component_clause,[],[f4586]) ).
fof(f55605,plain,
( spl22_1455
| ~ spl22_52
| ~ spl22_383 ),
inference(avatar_split_clause,[],[f4820,f4574,f498,f55603]) ).
fof(f55603,plain,
( spl22_1455
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,sK10(powerset(powerset(X10)))),X9)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1455])]) ).
fof(f4574,plain,
( spl22_383
<=> ! [X20,X21,X19] :
( element(sK13(X19,X20,sK10(powerset(X21))),X20)
| sP2(X19,X20,sK10(powerset(X21)))
| element(sK13(X19,X20,sK10(powerset(X21))),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_383])]) ).
fof(f4820,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK10(powerset(powerset(X10)))),X9)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) )
| ~ spl22_52
| ~ spl22_383 ),
inference(resolution,[],[f4575,f499]) ).
fof(f4575,plain,
( ! [X21,X19,X20] :
( element(sK13(X19,X20,sK10(powerset(X21))),X21)
| element(sK13(X19,X20,sK10(powerset(X21))),X20)
| sP2(X19,X20,sK10(powerset(X21))) )
| ~ spl22_383 ),
inference(avatar_component_clause,[],[f4574]) ).
fof(f55601,plain,
( spl22_1454
| ~ spl22_52
| ~ spl22_381 ),
inference(avatar_split_clause,[],[f4765,f4566,f498,f55599]) ).
fof(f55599,plain,
( spl22_1454
<=> ! [X9,X8,X10] :
( element(sK13(X8,sK10(powerset(powerset(X9))),X10),X10)
| sP2(X8,sK10(powerset(powerset(X9))),X10)
| subset(sK13(X8,sK10(powerset(powerset(X9))),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1454])]) ).
fof(f4566,plain,
( spl22_381
<=> ! [X20,X18,X19] :
( element(sK13(X18,sK10(powerset(X19)),X20),X20)
| sP2(X18,sK10(powerset(X19)),X20)
| element(sK13(X18,sK10(powerset(X19)),X20),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_381])]) ).
fof(f4765,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,sK10(powerset(powerset(X9))),X10),X10)
| sP2(X8,sK10(powerset(powerset(X9))),X10)
| subset(sK13(X8,sK10(powerset(powerset(X9))),X10),X9) )
| ~ spl22_52
| ~ spl22_381 ),
inference(resolution,[],[f4567,f499]) ).
fof(f4567,plain,
( ! [X18,X19,X20] :
( element(sK13(X18,sK10(powerset(X19)),X20),X20)
| element(sK13(X18,sK10(powerset(X19)),X20),X19)
| sP2(X18,sK10(powerset(X19)),X20) )
| ~ spl22_381 ),
inference(avatar_component_clause,[],[f4566]) ).
fof(f55597,plain,
( spl22_1453
| ~ spl22_52
| ~ spl22_379 ),
inference(avatar_split_clause,[],[f4686,f4558,f498,f55595]) ).
fof(f55595,plain,
( spl22_1453
<=> ! [X9,X8,X10] :
( in(sK13(sK10(powerset(powerset(X8))),X9,X10),X10)
| sP2(sK10(powerset(powerset(X8))),X9,X10)
| subset(sK13(sK10(powerset(powerset(X8))),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1453])]) ).
fof(f4558,plain,
( spl22_379
<=> ! [X16,X14,X15] :
( element(sK13(sK10(powerset(X14)),X15,X16),X14)
| in(sK13(sK10(powerset(X14)),X15,X16),X16)
| sP2(sK10(powerset(X14)),X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_379])]) ).
fof(f4686,plain,
( ! [X10,X8,X9] :
( in(sK13(sK10(powerset(powerset(X8))),X9,X10),X10)
| sP2(sK10(powerset(powerset(X8))),X9,X10)
| subset(sK13(sK10(powerset(powerset(X8))),X9,X10),X8) )
| ~ spl22_52
| ~ spl22_379 ),
inference(resolution,[],[f4559,f499]) ).
fof(f4559,plain,
( ! [X16,X14,X15] :
( element(sK13(sK10(powerset(X14)),X15,X16),X14)
| in(sK13(sK10(powerset(X14)),X15,X16),X16)
| sP2(sK10(powerset(X14)),X15,X16) )
| ~ spl22_379 ),
inference(avatar_component_clause,[],[f4558]) ).
fof(f55593,plain,
( spl22_1452
| ~ spl22_52
| ~ spl22_378 ),
inference(avatar_split_clause,[],[f4657,f4554,f498,f55591]) ).
fof(f55591,plain,
( spl22_1452
<=> ! [X9,X8,X10] :
( in(sK13(X8,sK10(powerset(powerset(X9))),X10),X10)
| sP2(X8,sK10(powerset(powerset(X9))),X10)
| subset(sK13(X8,sK10(powerset(powerset(X9))),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1452])]) ).
fof(f4554,plain,
( spl22_378
<=> ! [X13,X12,X11] :
( element(sK13(X11,sK10(powerset(X12)),X13),X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_378])]) ).
fof(f4657,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,sK10(powerset(powerset(X9))),X10),X10)
| sP2(X8,sK10(powerset(powerset(X9))),X10)
| subset(sK13(X8,sK10(powerset(powerset(X9))),X10),X9) )
| ~ spl22_52
| ~ spl22_378 ),
inference(resolution,[],[f4555,f499]) ).
fof(f4555,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK10(powerset(X12)),X13),X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13) )
| ~ spl22_378 ),
inference(avatar_component_clause,[],[f4554]) ).
fof(f55589,plain,
( spl22_1451
| ~ spl22_52
| ~ spl22_377 ),
inference(avatar_split_clause,[],[f4628,f4550,f498,f55587]) ).
fof(f55587,plain,
( spl22_1451
<=> ! [X9,X8,X10] :
( in(sK13(X8,X9,sK10(powerset(powerset(X10)))),X9)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1451])]) ).
fof(f4550,plain,
( spl22_377
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,sK10(powerset(X10))),X10)
| in(sK13(X8,X9,sK10(powerset(X10))),X9)
| sP2(X8,X9,sK10(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_377])]) ).
fof(f4628,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,X9,sK10(powerset(powerset(X10)))),X9)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) )
| ~ spl22_52
| ~ spl22_377 ),
inference(resolution,[],[f4551,f499]) ).
fof(f4551,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK10(powerset(X10))),X10)
| in(sK13(X8,X9,sK10(powerset(X10))),X9)
| sP2(X8,X9,sK10(powerset(X10))) )
| ~ spl22_377 ),
inference(avatar_component_clause,[],[f4550]) ).
fof(f55585,plain,
( spl22_1450
| ~ spl22_52
| ~ spl22_376 ),
inference(avatar_split_clause,[],[f4599,f4546,f498,f55583]) ).
fof(f55583,plain,
( spl22_1450
<=> ! [X9,X8,X10] :
( in(sK13(X8,X9,sK10(powerset(powerset(X10)))),X8)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1450])]) ).
fof(f4546,plain,
( spl22_376
<=> ! [X6,X5,X7] :
( element(sK13(X5,X6,sK10(powerset(X7))),X7)
| in(sK13(X5,X6,sK10(powerset(X7))),X5)
| sP2(X5,X6,sK10(powerset(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_376])]) ).
fof(f4599,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,X9,sK10(powerset(powerset(X10)))),X8)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) )
| ~ spl22_52
| ~ spl22_376 ),
inference(resolution,[],[f4547,f499]) ).
fof(f4547,plain,
( ! [X6,X7,X5] :
( element(sK13(X5,X6,sK10(powerset(X7))),X7)
| in(sK13(X5,X6,sK10(powerset(X7))),X5)
| sP2(X5,X6,sK10(powerset(X7))) )
| ~ spl22_376 ),
inference(avatar_component_clause,[],[f4546]) ).
fof(f55581,plain,
( spl22_1449
| ~ spl22_52
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4534,f4168,f498,f55579]) ).
fof(f55579,plain,
( spl22_1449
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,sK6(powerset(X10))),X8)
| sP2(X8,X9,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1449])]) ).
fof(f4168,plain,
( spl22_374
<=> ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X16)
| sP2(X16,X17,sK6(X18))
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_374])]) ).
fof(f4534,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK6(powerset(X10))),X8)
| sP2(X8,X9,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) )
| ~ spl22_52
| ~ spl22_374 ),
inference(resolution,[],[f4169,f499]) ).
fof(f4169,plain,
( ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X18)
| element(sK13(X16,X17,sK6(X18)),X16)
| sP2(X16,X17,sK6(X18))
| empty(X18) )
| ~ spl22_374 ),
inference(avatar_component_clause,[],[f4168]) ).
fof(f55577,plain,
( spl22_476
| ~ spl22_1448
| ~ spl22_822
| ~ spl22_1427 ),
inference(avatar_split_clause,[],[f55532,f55209,f14844,f55574,f6536]) ).
fof(f6536,plain,
( spl22_476
<=> empty(sK7(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_476])]) ).
fof(f55574,plain,
( spl22_1448
<=> sP0(sK5,sK6(sK7(sK5,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1448])]) ).
fof(f14844,plain,
( spl22_822
<=> ! [X5] :
( ~ sP0(sK5,sK6(X5))
| empty(X5)
| in(sK7(sK5,sK15),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_822])]) ).
fof(f55209,plain,
( spl22_1427
<=> ! [X1] :
( empty(X1)
| ~ sP0(sK5,sK6(X1))
| ~ in(X1,sK7(sK5,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1427])]) ).
fof(f55532,plain,
( ~ sP0(sK5,sK6(sK7(sK5,sK15)))
| empty(sK7(sK5,sK15))
| ~ spl22_822
| ~ spl22_1427 ),
inference(duplicate_literal_removal,[],[f55276]) ).
fof(f55276,plain,
( ~ sP0(sK5,sK6(sK7(sK5,sK15)))
| empty(sK7(sK5,sK15))
| empty(sK7(sK5,sK15))
| ~ sP0(sK5,sK6(sK7(sK5,sK15)))
| ~ spl22_822
| ~ spl22_1427 ),
inference(resolution,[],[f55210,f14845]) ).
fof(f14845,plain,
( ! [X5] :
( in(sK7(sK5,sK15),X5)
| empty(X5)
| ~ sP0(sK5,sK6(X5)) )
| ~ spl22_822 ),
inference(avatar_component_clause,[],[f14844]) ).
fof(f55210,plain,
( ! [X1] :
( ~ in(X1,sK7(sK5,sK15))
| ~ sP0(sK5,sK6(X1))
| empty(X1) )
| ~ spl22_1427 ),
inference(avatar_component_clause,[],[f55209]) ).
fof(f55572,plain,
( spl22_1447
| ~ spl22_153
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4451,f4164,f1395,f55570]) ).
fof(f55570,plain,
( spl22_1447
<=> ! [X4,X0,X3,X2,X1] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1447])]) ).
fof(f1395,plain,
( spl22_153
<=> ! [X2,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_153])]) ).
fof(f4164,plain,
( spl22_373
<=> ! [X2,X0,X1,X3] :
( in(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_373])]) ).
fof(f4451,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(powerset(X0),X1,X2)) )
| ~ spl22_153
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1396]) ).
fof(f1396,plain,
( ! [X2,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2) )
| ~ spl22_153 ),
inference(avatar_component_clause,[],[f1395]) ).
fof(f4165,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(powerset(X0),X1,X2))
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| in(sK13(powerset(X0),X1,X2),X2) )
| ~ spl22_373 ),
inference(avatar_component_clause,[],[f4164]) ).
fof(f55568,plain,
( spl22_1446
| ~ spl22_52
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4447,f4160,f498,f55566]) ).
fof(f55566,plain,
( spl22_1446
<=> ! [X9,X8,X10] :
( element(sK13(sK6(powerset(X8)),X9,X10),X10)
| sP2(sK6(powerset(X8)),X9,X10)
| empty(powerset(X8))
| subset(sK13(sK6(powerset(X8)),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1446])]) ).
fof(f4160,plain,
( spl22_372
<=> ! [X16,X17,X15] :
( element(sK13(sK6(X15),X16,X17),X17)
| sP2(sK6(X15),X16,X17)
| element(sK13(sK6(X15),X16,X17),X15)
| empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_372])]) ).
fof(f4447,plain,
( ! [X10,X8,X9] :
( element(sK13(sK6(powerset(X8)),X9,X10),X10)
| sP2(sK6(powerset(X8)),X9,X10)
| empty(powerset(X8))
| subset(sK13(sK6(powerset(X8)),X9,X10),X8) )
| ~ spl22_52
| ~ spl22_372 ),
inference(resolution,[],[f4161,f499]) ).
fof(f4161,plain,
( ! [X16,X17,X15] :
( element(sK13(sK6(X15),X16,X17),X17)
| element(sK13(sK6(X15),X16,X17),X15)
| sP2(sK6(X15),X16,X17)
| empty(X15) )
| ~ spl22_372 ),
inference(avatar_component_clause,[],[f4160]) ).
fof(f55564,plain,
( spl22_1445
| ~ spl22_153
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4400,f4156,f1395,f55562]) ).
fof(f55562,plain,
( spl22_1445
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1445])]) ).
fof(f4156,plain,
( spl22_371
<=> ! [X2,X0,X1,X3] :
( in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_371])]) ).
fof(f4400,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(X0,X1,powerset(X2))) )
| ~ spl22_153
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1396]) ).
fof(f4157,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,X1,powerset(X2)))
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X0) )
| ~ spl22_371 ),
inference(avatar_component_clause,[],[f4156]) ).
fof(f55560,plain,
( spl22_1444
| ~ spl22_52
| ~ spl22_370 ),
inference(avatar_split_clause,[],[f4392,f4152,f498,f55558]) ).
fof(f55558,plain,
( spl22_1444
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,sK6(powerset(X10))),X9)
| sP2(X8,X9,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1444])]) ).
fof(f4152,plain,
( spl22_370
<=> ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X17)
| sP2(X16,X17,sK6(X18))
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_370])]) ).
fof(f4392,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK6(powerset(X10))),X9)
| sP2(X8,X9,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) )
| ~ spl22_52
| ~ spl22_370 ),
inference(resolution,[],[f4153,f499]) ).
fof(f4153,plain,
( ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X18)
| element(sK13(X16,X17,sK6(X18)),X17)
| sP2(X16,X17,sK6(X18))
| empty(X18) )
| ~ spl22_370 ),
inference(avatar_component_clause,[],[f4152]) ).
fof(f55556,plain,
( spl22_1443
| ~ spl22_153
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4349,f4148,f1395,f55554]) ).
fof(f55554,plain,
( spl22_1443
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1443])]) ).
fof(f4148,plain,
( spl22_369
<=> ! [X2,X0,X1,X3] :
( in(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_369])]) ).
fof(f4349,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(X0,powerset(X1),X2)) )
| ~ spl22_153
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1396]) ).
fof(f4149,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,powerset(X1),X2))
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| in(sK13(X0,powerset(X1),X2),X2) )
| ~ spl22_369 ),
inference(avatar_component_clause,[],[f4148]) ).
fof(f55552,plain,
( spl22_1442
| ~ spl22_52
| ~ spl22_368 ),
inference(avatar_split_clause,[],[f4345,f4144,f498,f55550]) ).
fof(f55550,plain,
( spl22_1442
<=> ! [X9,X8,X10] :
( element(sK13(X8,sK6(powerset(X9)),X10),X10)
| sP2(X8,sK6(powerset(X9)),X10)
| empty(powerset(X9))
| subset(sK13(X8,sK6(powerset(X9)),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1442])]) ).
fof(f4144,plain,
( spl22_368
<=> ! [X16,X17,X15] :
( element(sK13(X15,sK6(X16),X17),X17)
| sP2(X15,sK6(X16),X17)
| element(sK13(X15,sK6(X16),X17),X16)
| empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_368])]) ).
fof(f4345,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,sK6(powerset(X9)),X10),X10)
| sP2(X8,sK6(powerset(X9)),X10)
| empty(powerset(X9))
| subset(sK13(X8,sK6(powerset(X9)),X10),X9) )
| ~ spl22_52
| ~ spl22_368 ),
inference(resolution,[],[f4145,f499]) ).
fof(f4145,plain,
( ! [X16,X17,X15] :
( element(sK13(X15,sK6(X16),X17),X17)
| element(sK13(X15,sK6(X16),X17),X16)
| sP2(X15,sK6(X16),X17)
| empty(X16) )
| ~ spl22_368 ),
inference(avatar_component_clause,[],[f4144]) ).
fof(f55548,plain,
( spl22_1441
| ~ spl22_153
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4298,f4139,f1395,f55546]) ).
fof(f55546,plain,
( spl22_1441
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1441])]) ).
fof(f4139,plain,
( spl22_367
<=> ! [X2,X0,X1,X3] :
( in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_367])]) ).
fof(f4298,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1)
| ~ in(X3,relation_dom(X4))
| ~ sP0(X4,sK13(X0,X1,powerset(X2))) )
| ~ spl22_153
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1396]) ).
fof(f4140,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,sK13(X0,X1,powerset(X2)))
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| in(sK13(X0,X1,powerset(X2)),X1) )
| ~ spl22_367 ),
inference(avatar_component_clause,[],[f4139]) ).
fof(f55544,plain,
( spl22_1440
| ~ spl22_52
| ~ spl22_365 ),
inference(avatar_split_clause,[],[f4255,f4131,f498,f55542]) ).
fof(f55542,plain,
( spl22_1440
<=> ! [X9,X8,X10] :
( in(sK13(sK6(powerset(X8)),X9,X10),X10)
| empty(powerset(X8))
| sP2(sK6(powerset(X8)),X9,X10)
| subset(sK13(sK6(powerset(X8)),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1440])]) ).
fof(f4131,plain,
( spl22_365
<=> ! [X16,X14,X15] :
( element(sK13(sK6(X14),X15,X16),X14)
| empty(X14)
| in(sK13(sK6(X14),X15,X16),X16)
| sP2(sK6(X14),X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_365])]) ).
fof(f4255,plain,
( ! [X10,X8,X9] :
( in(sK13(sK6(powerset(X8)),X9,X10),X10)
| empty(powerset(X8))
| sP2(sK6(powerset(X8)),X9,X10)
| subset(sK13(sK6(powerset(X8)),X9,X10),X8) )
| ~ spl22_52
| ~ spl22_365 ),
inference(resolution,[],[f4132,f499]) ).
fof(f4132,plain,
( ! [X16,X14,X15] :
( element(sK13(sK6(X14),X15,X16),X14)
| in(sK13(sK6(X14),X15,X16),X16)
| empty(X14)
| sP2(sK6(X14),X15,X16) )
| ~ spl22_365 ),
inference(avatar_component_clause,[],[f4131]) ).
fof(f55540,plain,
( spl22_1439
| ~ spl22_52
| ~ spl22_364 ),
inference(avatar_split_clause,[],[f4229,f4127,f498,f55538]) ).
fof(f55538,plain,
( spl22_1439
<=> ! [X9,X8,X10] :
( in(sK13(X8,sK6(powerset(X9)),X10),X10)
| empty(powerset(X9))
| sP2(X8,sK6(powerset(X9)),X10)
| subset(sK13(X8,sK6(powerset(X9)),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1439])]) ).
fof(f4127,plain,
( spl22_364
<=> ! [X13,X12,X11] :
( element(sK13(X11,sK6(X12),X13),X12)
| empty(X12)
| in(sK13(X11,sK6(X12),X13),X13)
| sP2(X11,sK6(X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_364])]) ).
fof(f4229,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,sK6(powerset(X9)),X10),X10)
| empty(powerset(X9))
| sP2(X8,sK6(powerset(X9)),X10)
| subset(sK13(X8,sK6(powerset(X9)),X10),X9) )
| ~ spl22_52
| ~ spl22_364 ),
inference(resolution,[],[f4128,f499]) ).
fof(f4128,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK6(X12),X13),X12)
| in(sK13(X11,sK6(X12),X13),X13)
| empty(X12)
| sP2(X11,sK6(X12),X13) )
| ~ spl22_364 ),
inference(avatar_component_clause,[],[f4127]) ).
fof(f55536,plain,
( spl22_1438
| ~ spl22_52
| ~ spl22_363 ),
inference(avatar_split_clause,[],[f4203,f4123,f498,f55534]) ).
fof(f55534,plain,
( spl22_1438
<=> ! [X9,X8,X10] :
( in(sK13(X8,X9,sK6(powerset(X10))),X9)
| empty(powerset(X10))
| sP2(X8,X9,sK6(powerset(X10)))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1438])]) ).
fof(f4123,plain,
( spl22_363
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,sK6(X10)),X10)
| empty(X10)
| in(sK13(X8,X9,sK6(X10)),X9)
| sP2(X8,X9,sK6(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_363])]) ).
fof(f4203,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,X9,sK6(powerset(X10))),X9)
| empty(powerset(X10))
| sP2(X8,X9,sK6(powerset(X10)))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) )
| ~ spl22_52
| ~ spl22_363 ),
inference(resolution,[],[f4124,f499]) ).
fof(f4124,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK6(X10)),X10)
| in(sK13(X8,X9,sK6(X10)),X9)
| empty(X10)
| sP2(X8,X9,sK6(X10)) )
| ~ spl22_363 ),
inference(avatar_component_clause,[],[f4123]) ).
fof(f55251,plain,
( spl22_1437
| ~ spl22_52
| ~ spl22_362 ),
inference(avatar_split_clause,[],[f4177,f4119,f498,f55249]) ).
fof(f55249,plain,
( spl22_1437
<=> ! [X9,X8,X10] :
( in(sK13(X8,X9,sK6(powerset(X10))),X8)
| empty(powerset(X10))
| sP2(X8,X9,sK6(powerset(X10)))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1437])]) ).
fof(f4119,plain,
( spl22_362
<=> ! [X6,X5,X7] :
( element(sK13(X5,X6,sK6(X7)),X7)
| empty(X7)
| in(sK13(X5,X6,sK6(X7)),X5)
| sP2(X5,X6,sK6(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_362])]) ).
fof(f4177,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,X9,sK6(powerset(X10))),X8)
| empty(powerset(X10))
| sP2(X8,X9,sK6(powerset(X10)))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) )
| ~ spl22_52
| ~ spl22_362 ),
inference(resolution,[],[f4120,f499]) ).
fof(f4120,plain,
( ! [X6,X7,X5] :
( element(sK13(X5,X6,sK6(X7)),X7)
| in(sK13(X5,X6,sK6(X7)),X5)
| empty(X7)
| sP2(X5,X6,sK6(X7)) )
| ~ spl22_362 ),
inference(avatar_component_clause,[],[f4119]) ).
fof(f55247,plain,
( spl22_1436
| ~ spl22_65
| ~ spl22_359 ),
inference(avatar_split_clause,[],[f4076,f4035,f610,f55245]) ).
fof(f55245,plain,
( spl22_1436
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(powerset(X1)))),relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1436])]) ).
fof(f610,plain,
( spl22_65
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_65])]) ).
fof(f4035,plain,
( spl22_359
<=> ! [X12,X11] :
( element(sK8(X11,sK10(powerset(X12))),relation_dom(X11))
| sP0(X11,sK10(powerset(X12)))
| element(sK7(X11,sK10(powerset(X12))),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_359])]) ).
fof(f4076,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK10(powerset(powerset(X1)))),relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl22_65
| ~ spl22_359 ),
inference(resolution,[],[f4036,f611]) ).
fof(f611,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl22_65 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f4036,plain,
( ! [X11,X12] :
( element(sK8(X11,sK10(powerset(X12))),relation_dom(X11))
| element(sK7(X11,sK10(powerset(X12))),X12)
| sP0(X11,sK10(powerset(X12))) )
| ~ spl22_359 ),
inference(avatar_component_clause,[],[f4035]) ).
fof(f55243,plain,
( spl22_1435
| ~ spl22_65
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4061,f4027,f610,f55241]) ).
fof(f55241,plain,
( spl22_1435
<=> ! [X2,X0,X1] :
( in(sK8(X0,sK10(powerset(powerset(X1)))),relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1435])]) ).
fof(f4027,plain,
( spl22_357
<=> ! [X2,X3] :
( element(sK7(X2,sK10(powerset(X3))),X3)
| in(sK8(X2,sK10(powerset(X3))),relation_dom(X2))
| sP0(X2,sK10(powerset(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_357])]) ).
fof(f4061,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,sK10(powerset(powerset(X1)))),relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl22_65
| ~ spl22_357 ),
inference(resolution,[],[f4028,f611]) ).
fof(f4028,plain,
( ! [X2,X3] :
( in(sK8(X2,sK10(powerset(X3))),relation_dom(X2))
| element(sK7(X2,sK10(powerset(X3))),X3)
| sP0(X2,sK10(powerset(X3))) )
| ~ spl22_357 ),
inference(avatar_component_clause,[],[f4027]) ).
fof(f55239,plain,
( spl22_1434
| ~ spl22_137
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4017,f3873,f1213,f55237]) ).
fof(f55237,plain,
( spl22_1434
<=> ! [X50,X52,X51] :
( subset(sK13(powerset(X50),X51,sK10(powerset(X52))),X50)
| sP2(powerset(X50),X51,sK10(powerset(X52)))
| element(sK13(powerset(X50),X51,sK10(powerset(X52))),X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1434])]) ).
fof(f1213,plain,
( spl22_137
<=> ! [X6,X5] :
( element(X5,X6)
| ~ in(X5,sK10(powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_137])]) ).
fof(f3873,plain,
( spl22_354
<=> ! [X9,X8,X10] :
( in(sK13(powerset(X8),X9,X10),X10)
| sP2(powerset(X8),X9,X10)
| subset(sK13(powerset(X8),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_354])]) ).
fof(f4017,plain,
( ! [X50,X51,X52] :
( subset(sK13(powerset(X50),X51,sK10(powerset(X52))),X50)
| sP2(powerset(X50),X51,sK10(powerset(X52)))
| element(sK13(powerset(X50),X51,sK10(powerset(X52))),X52) )
| ~ spl22_137
| ~ spl22_354 ),
inference(resolution,[],[f3874,f1214]) ).
fof(f1214,plain,
( ! [X6,X5] :
( ~ in(X5,sK10(powerset(X6)))
| element(X5,X6) )
| ~ spl22_137 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f3874,plain,
( ! [X10,X8,X9] :
( subset(sK13(powerset(X8),X9,X10),X8)
| in(sK13(powerset(X8),X9,X10),X10)
| sP2(powerset(X8),X9,X10) )
| ~ spl22_354 ),
inference(avatar_component_clause,[],[f3873]) ).
fof(f55235,plain,
( spl22_1433
| ~ spl22_237
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4009,f3873,f2435,f55233]) ).
fof(f55233,plain,
( spl22_1433
<=> ! [X24,X21,X23,X22] :
( subset(sK13(powerset(X21),X22,set_intersection2(X23,X24)),X21)
| sP2(powerset(X21),X22,set_intersection2(X23,X24))
| in(sK13(powerset(X21),X22,set_intersection2(X23,X24)),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1433])]) ).
fof(f2435,plain,
( spl22_237
<=> ! [X4,X5,X3] :
( ~ in(X3,set_intersection2(X4,X5))
| in(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_237])]) ).
fof(f4009,plain,
( ! [X21,X24,X22,X23] :
( subset(sK13(powerset(X21),X22,set_intersection2(X23,X24)),X21)
| sP2(powerset(X21),X22,set_intersection2(X23,X24))
| in(sK13(powerset(X21),X22,set_intersection2(X23,X24)),X24) )
| ~ spl22_237
| ~ spl22_354 ),
inference(resolution,[],[f3874,f2436]) ).
fof(f2436,plain,
( ! [X3,X4,X5] :
( ~ in(X3,set_intersection2(X4,X5))
| in(X3,X5) )
| ~ spl22_237 ),
inference(avatar_component_clause,[],[f2435]) ).
fof(f55231,plain,
( spl22_1432
| ~ spl22_238
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4008,f3873,f2439,f55229]) ).
fof(f55229,plain,
( spl22_1432
<=> ! [X18,X20,X17,X19] :
( subset(sK13(powerset(X17),X18,set_intersection2(X19,X20)),X17)
| sP2(powerset(X17),X18,set_intersection2(X19,X20))
| in(sK13(powerset(X17),X18,set_intersection2(X19,X20)),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1432])]) ).
fof(f2439,plain,
( spl22_238
<=> ! [X6,X8,X7] :
( ~ in(X6,set_intersection2(X7,X8))
| in(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_238])]) ).
fof(f4008,plain,
( ! [X18,X19,X17,X20] :
( subset(sK13(powerset(X17),X18,set_intersection2(X19,X20)),X17)
| sP2(powerset(X17),X18,set_intersection2(X19,X20))
| in(sK13(powerset(X17),X18,set_intersection2(X19,X20)),X19) )
| ~ spl22_238
| ~ spl22_354 ),
inference(resolution,[],[f3874,f2440]) ).
fof(f2440,plain,
( ! [X8,X6,X7] :
( ~ in(X6,set_intersection2(X7,X8))
| in(X6,X7) )
| ~ spl22_238 ),
inference(avatar_component_clause,[],[f2439]) ).
fof(f55227,plain,
( spl22_1431
| ~ spl22_137
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3995,f3869,f1213,f55225]) ).
fof(f55225,plain,
( spl22_1431
<=> ! [X50,X51,X49] :
( subset(sK13(sK10(powerset(X49)),X50,powerset(X51)),X51)
| sP2(sK10(powerset(X49)),X50,powerset(X51))
| element(sK13(sK10(powerset(X49)),X50,powerset(X51)),X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1431])]) ).
fof(f3869,plain,
( spl22_353
<=> ! [X9,X8,X10] :
( in(sK13(X8,X9,powerset(X10)),X8)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_353])]) ).
fof(f3995,plain,
( ! [X50,X51,X49] :
( subset(sK13(sK10(powerset(X49)),X50,powerset(X51)),X51)
| sP2(sK10(powerset(X49)),X50,powerset(X51))
| element(sK13(sK10(powerset(X49)),X50,powerset(X51)),X49) )
| ~ spl22_137
| ~ spl22_353 ),
inference(resolution,[],[f3870,f1214]) ).
fof(f3870,plain,
( ! [X10,X8,X9] :
( subset(sK13(X8,X9,powerset(X10)),X10)
| in(sK13(X8,X9,powerset(X10)),X8)
| sP2(X8,X9,powerset(X10)) )
| ~ spl22_353 ),
inference(avatar_component_clause,[],[f3869]) ).
fof(f55223,plain,
( spl22_1430
| ~ spl22_237
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3987,f3869,f2435,f55221]) ).
fof(f55221,plain,
( spl22_1430
<=> ! [X20,X21,X23,X22] :
( subset(sK13(set_intersection2(X20,X21),X22,powerset(X23)),X23)
| sP2(set_intersection2(X20,X21),X22,powerset(X23))
| in(sK13(set_intersection2(X20,X21),X22,powerset(X23)),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1430])]) ).
fof(f3987,plain,
( ! [X21,X22,X23,X20] :
( subset(sK13(set_intersection2(X20,X21),X22,powerset(X23)),X23)
| sP2(set_intersection2(X20,X21),X22,powerset(X23))
| in(sK13(set_intersection2(X20,X21),X22,powerset(X23)),X21) )
| ~ spl22_237
| ~ spl22_353 ),
inference(resolution,[],[f3870,f2436]) ).
fof(f55219,plain,
( spl22_1429
| ~ spl22_238
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3986,f3869,f2439,f55217]) ).
fof(f55217,plain,
( spl22_1429
<=> ! [X18,X17,X16,X19] :
( subset(sK13(set_intersection2(X16,X17),X18,powerset(X19)),X19)
| sP2(set_intersection2(X16,X17),X18,powerset(X19))
| in(sK13(set_intersection2(X16,X17),X18,powerset(X19)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1429])]) ).
fof(f3986,plain,
( ! [X18,X19,X16,X17] :
( subset(sK13(set_intersection2(X16,X17),X18,powerset(X19)),X19)
| sP2(set_intersection2(X16,X17),X18,powerset(X19))
| in(sK13(set_intersection2(X16,X17),X18,powerset(X19)),X16) )
| ~ spl22_238
| ~ spl22_353 ),
inference(resolution,[],[f3870,f2440]) ).
fof(f55215,plain,
( spl22_1428
| ~ spl22_137
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3973,f3865,f1213,f55213]) ).
fof(f55213,plain,
( spl22_1428
<=> ! [X52,X50,X51] :
( subset(sK13(X50,powerset(X51),sK10(powerset(X52))),X51)
| sP2(X50,powerset(X51),sK10(powerset(X52)))
| element(sK13(X50,powerset(X51),sK10(powerset(X52))),X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1428])]) ).
fof(f3865,plain,
( spl22_352
<=> ! [X9,X8,X10] :
( in(sK13(X8,powerset(X9),X10),X10)
| sP2(X8,powerset(X9),X10)
| subset(sK13(X8,powerset(X9),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_352])]) ).
fof(f3973,plain,
( ! [X50,X51,X52] :
( subset(sK13(X50,powerset(X51),sK10(powerset(X52))),X51)
| sP2(X50,powerset(X51),sK10(powerset(X52)))
| element(sK13(X50,powerset(X51),sK10(powerset(X52))),X52) )
| ~ spl22_137
| ~ spl22_352 ),
inference(resolution,[],[f3866,f1214]) ).
fof(f3866,plain,
( ! [X10,X8,X9] :
( subset(sK13(X8,powerset(X9),X10),X9)
| in(sK13(X8,powerset(X9),X10),X10)
| sP2(X8,powerset(X9),X10) )
| ~ spl22_352 ),
inference(avatar_component_clause,[],[f3865]) ).
fof(f55211,plain,
( spl22_1427
| ~ spl22_45
| ~ spl22_822 ),
inference(avatar_split_clause,[],[f45265,f14844,f448,f55209]) ).
fof(f45265,plain,
( ! [X1] :
( empty(X1)
| ~ sP0(sK5,sK6(X1))
| ~ in(X1,sK7(sK5,sK15)) )
| ~ spl22_45
| ~ spl22_822 ),
inference(resolution,[],[f14845,f449]) ).
fof(f55207,plain,
( spl22_1426
| ~ spl22_237
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3965,f3865,f2435,f55205]) ).
fof(f55205,plain,
( spl22_1426
<=> ! [X24,X21,X23,X22] :
( subset(sK13(X21,powerset(X22),set_intersection2(X23,X24)),X22)
| sP2(X21,powerset(X22),set_intersection2(X23,X24))
| in(sK13(X21,powerset(X22),set_intersection2(X23,X24)),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1426])]) ).
fof(f3965,plain,
( ! [X21,X24,X22,X23] :
( subset(sK13(X21,powerset(X22),set_intersection2(X23,X24)),X22)
| sP2(X21,powerset(X22),set_intersection2(X23,X24))
| in(sK13(X21,powerset(X22),set_intersection2(X23,X24)),X24) )
| ~ spl22_237
| ~ spl22_352 ),
inference(resolution,[],[f3866,f2436]) ).
fof(f55203,plain,
( spl22_1425
| ~ spl22_238
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3964,f3865,f2439,f55201]) ).
fof(f55201,plain,
( spl22_1425
<=> ! [X18,X20,X17,X19] :
( subset(sK13(X17,powerset(X18),set_intersection2(X19,X20)),X18)
| sP2(X17,powerset(X18),set_intersection2(X19,X20))
| in(sK13(X17,powerset(X18),set_intersection2(X19,X20)),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1425])]) ).
fof(f3964,plain,
( ! [X18,X19,X17,X20] :
( subset(sK13(X17,powerset(X18),set_intersection2(X19,X20)),X18)
| sP2(X17,powerset(X18),set_intersection2(X19,X20))
| in(sK13(X17,powerset(X18),set_intersection2(X19,X20)),X19) )
| ~ spl22_238
| ~ spl22_352 ),
inference(resolution,[],[f3866,f2440]) ).
fof(f55199,plain,
( spl22_1424
| ~ spl22_137
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3951,f3861,f1213,f55197]) ).
fof(f55197,plain,
( spl22_1424
<=> ! [X52,X50,X51] :
( subset(sK13(X50,sK10(powerset(X51)),powerset(X52)),X52)
| sP2(X50,sK10(powerset(X51)),powerset(X52))
| element(sK13(X50,sK10(powerset(X51)),powerset(X52)),X51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1424])]) ).
fof(f3861,plain,
( spl22_351
<=> ! [X9,X8,X10] :
( in(sK13(X8,X9,powerset(X10)),X9)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_351])]) ).
fof(f3951,plain,
( ! [X50,X51,X52] :
( subset(sK13(X50,sK10(powerset(X51)),powerset(X52)),X52)
| sP2(X50,sK10(powerset(X51)),powerset(X52))
| element(sK13(X50,sK10(powerset(X51)),powerset(X52)),X51) )
| ~ spl22_137
| ~ spl22_351 ),
inference(resolution,[],[f3862,f1214]) ).
fof(f3862,plain,
( ! [X10,X8,X9] :
( subset(sK13(X8,X9,powerset(X10)),X10)
| in(sK13(X8,X9,powerset(X10)),X9)
| sP2(X8,X9,powerset(X10)) )
| ~ spl22_351 ),
inference(avatar_component_clause,[],[f3861]) ).
fof(f55195,plain,
( spl22_1423
| ~ spl22_237
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3943,f3861,f2435,f55193]) ).
fof(f55193,plain,
( spl22_1423
<=> ! [X24,X21,X23,X22] :
( subset(sK13(X21,set_intersection2(X22,X23),powerset(X24)),X24)
| sP2(X21,set_intersection2(X22,X23),powerset(X24))
| in(sK13(X21,set_intersection2(X22,X23),powerset(X24)),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1423])]) ).
fof(f3943,plain,
( ! [X21,X24,X22,X23] :
( subset(sK13(X21,set_intersection2(X22,X23),powerset(X24)),X24)
| sP2(X21,set_intersection2(X22,X23),powerset(X24))
| in(sK13(X21,set_intersection2(X22,X23),powerset(X24)),X23) )
| ~ spl22_237
| ~ spl22_351 ),
inference(resolution,[],[f3862,f2436]) ).
fof(f55191,plain,
( spl22_1422
| ~ spl22_238
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3942,f3861,f2439,f55189]) ).
fof(f55189,plain,
( spl22_1422
<=> ! [X18,X20,X17,X19] :
( subset(sK13(X17,set_intersection2(X18,X19),powerset(X20)),X20)
| sP2(X17,set_intersection2(X18,X19),powerset(X20))
| in(sK13(X17,set_intersection2(X18,X19),powerset(X20)),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1422])]) ).
fof(f3942,plain,
( ! [X18,X19,X17,X20] :
( subset(sK13(X17,set_intersection2(X18,X19),powerset(X20)),X20)
| sP2(X17,set_intersection2(X18,X19),powerset(X20))
| in(sK13(X17,set_intersection2(X18,X19),powerset(X20)),X18) )
| ~ spl22_238
| ~ spl22_351 ),
inference(resolution,[],[f3862,f2440]) ).
fof(f55187,plain,
( spl22_1421
| ~ spl22_65
| ~ spl22_349 ),
inference(avatar_split_clause,[],[f3890,f3853,f610,f55185]) ).
fof(f55185,plain,
( spl22_1421
<=> ! [X2,X0,X1] :
( element(sK8(X0,sK6(powerset(X1))),relation_dom(X0))
| sP0(X0,sK6(powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1421])]) ).
fof(f3853,plain,
( spl22_349
<=> ! [X9,X10] :
( element(sK8(X9,sK6(X10)),relation_dom(X9))
| sP0(X9,sK6(X10))
| element(sK7(X9,sK6(X10)),X10)
| empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_349])]) ).
fof(f3890,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,sK6(powerset(X1))),relation_dom(X0))
| sP0(X0,sK6(powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl22_65
| ~ spl22_349 ),
inference(resolution,[],[f3854,f611]) ).
fof(f3854,plain,
( ! [X10,X9] :
( element(sK8(X9,sK6(X10)),relation_dom(X9))
| element(sK7(X9,sK6(X10)),X10)
| sP0(X9,sK6(X10))
| empty(X10) )
| ~ spl22_349 ),
inference(avatar_component_clause,[],[f3853]) ).
fof(f55183,plain,
( spl22_1420
| ~ spl22_65
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3883,f3849,f610,f55181]) ).
fof(f55181,plain,
( spl22_1420
<=> ! [X2,X0,X1] :
( in(sK8(X0,sK6(powerset(X1))),relation_dom(X0))
| empty(powerset(X1))
| sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1420])]) ).
fof(f3849,plain,
( spl22_348
<=> ! [X2,X3] :
( element(sK7(X2,sK6(X3)),X3)
| empty(X3)
| in(sK8(X2,sK6(X3)),relation_dom(X2))
| sP0(X2,sK6(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_348])]) ).
fof(f3883,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,sK6(powerset(X1))),relation_dom(X0))
| empty(powerset(X1))
| sP0(X0,sK6(powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl22_65
| ~ spl22_348 ),
inference(resolution,[],[f3850,f611]) ).
fof(f3850,plain,
( ! [X2,X3] :
( in(sK8(X2,sK6(X3)),relation_dom(X2))
| element(sK7(X2,sK6(X3)),X3)
| empty(X3)
| sP0(X2,sK6(X3)) )
| ~ spl22_348 ),
inference(avatar_component_clause,[],[f3849]) ).
fof(f55179,plain,
( spl22_1419
| ~ spl22_67
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f3839,f3831,f633,f55177]) ).
fof(f55177,plain,
( spl22_1419
<=> ! [X4,X5,X3] :
( sP2(sK10(powerset(powerset(X3))),X4,sK10(powerset(powerset(X3))))
| element(X5,X3)
| ~ in(X5,sK13(sK10(powerset(powerset(X3))),X4,sK10(powerset(powerset(X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1419])]) ).
fof(f633,plain,
( spl22_67
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_67])]) ).
fof(f3831,plain,
( spl22_347
<=> ! [X13,X14] :
( sP2(sK10(powerset(X13)),X14,sK10(powerset(X13)))
| element(sK13(sK10(powerset(X13)),X14,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_347])]) ).
fof(f3839,plain,
( ! [X3,X4,X5] :
( sP2(sK10(powerset(powerset(X3))),X4,sK10(powerset(powerset(X3))))
| element(X5,X3)
| ~ in(X5,sK13(sK10(powerset(powerset(X3))),X4,sK10(powerset(powerset(X3))))) )
| ~ spl22_67
| ~ spl22_347 ),
inference(resolution,[],[f3832,f634]) ).
fof(f634,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl22_67 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f3832,plain,
( ! [X14,X13] :
( element(sK13(sK10(powerset(X13)),X14,sK10(powerset(X13))),X13)
| sP2(sK10(powerset(X13)),X14,sK10(powerset(X13))) )
| ~ spl22_347 ),
inference(avatar_component_clause,[],[f3831]) ).
fof(f55175,plain,
( spl22_1418
| ~ spl22_67
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f3835,f3827,f633,f55173]) ).
fof(f55173,plain,
( spl22_1418
<=> ! [X4,X5,X3] :
( sP2(X3,sK10(powerset(powerset(X4))),sK10(powerset(powerset(X4))))
| element(X5,X4)
| ~ in(X5,sK13(X3,sK10(powerset(powerset(X4))),sK10(powerset(powerset(X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1418])]) ).
fof(f3827,plain,
( spl22_346
<=> ! [X13,X14] :
( sP2(X13,sK10(powerset(X14)),sK10(powerset(X14)))
| element(sK13(X13,sK10(powerset(X14)),sK10(powerset(X14))),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_346])]) ).
fof(f3835,plain,
( ! [X3,X4,X5] :
( sP2(X3,sK10(powerset(powerset(X4))),sK10(powerset(powerset(X4))))
| element(X5,X4)
| ~ in(X5,sK13(X3,sK10(powerset(powerset(X4))),sK10(powerset(powerset(X4))))) )
| ~ spl22_67
| ~ spl22_346 ),
inference(resolution,[],[f3828,f634]) ).
fof(f3828,plain,
( ! [X14,X13] :
( element(sK13(X13,sK10(powerset(X14)),sK10(powerset(X14))),X14)
| sP2(X13,sK10(powerset(X14)),sK10(powerset(X14))) )
| ~ spl22_346 ),
inference(avatar_component_clause,[],[f3827]) ).
fof(f55171,plain,
( spl22_1417
| ~ spl22_59
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3785,f3750,f552,f55169]) ).
fof(f55169,plain,
( spl22_1417
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(set_intersection2(X0,X1),powerset(X2)),sK15) = apply(set_intersection2(X0,X1),sK15)
| ~ function(set_intersection2(X0,X1))
| empty(powerset(X2))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1417])]) ).
fof(f552,plain,
( spl22_59
<=> ! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_59])]) ).
fof(f3750,plain,
( spl22_342
<=> ! [X2,X1] :
( empty(powerset(X1))
| apply(relation_dom_restriction(X2,powerset(X1)),sK15) = apply(X2,sK15)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_342])]) ).
fof(f3785,plain,
( ! [X2,X0,X1] :
( apply(relation_dom_restriction(set_intersection2(X0,X1),powerset(X2)),sK15) = apply(set_intersection2(X0,X1),sK15)
| ~ function(set_intersection2(X0,X1))
| empty(powerset(X2))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_342 ),
inference(resolution,[],[f3751,f553]) ).
fof(f553,plain,
( ! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f3751,plain,
( ! [X2,X1] :
( ~ relation(X2)
| apply(relation_dom_restriction(X2,powerset(X1)),sK15) = apply(X2,sK15)
| ~ function(X2)
| empty(powerset(X1)) )
| ~ spl22_342 ),
inference(avatar_component_clause,[],[f3750]) ).
fof(f55165,plain,
( spl22_1416
| ~ spl22_59
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3766,f3746,f552,f55163]) ).
fof(f55163,plain,
( spl22_1416
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(set_intersection2(X0,X1),X2),sK10(X2)) = apply(set_intersection2(X0,X1),sK10(X2))
| ~ function(set_intersection2(X0,X1))
| empty(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1416])]) ).
fof(f3746,plain,
( spl22_341
<=> ! [X2,X1] :
( empty(X1)
| apply(relation_dom_restriction(X2,X1),sK10(X1)) = apply(X2,sK10(X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_341])]) ).
fof(f3766,plain,
( ! [X2,X0,X1] :
( apply(relation_dom_restriction(set_intersection2(X0,X1),X2),sK10(X2)) = apply(set_intersection2(X0,X1),sK10(X2))
| ~ function(set_intersection2(X0,X1))
| empty(X2)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_341 ),
inference(resolution,[],[f3747,f553]) ).
fof(f3747,plain,
( ! [X2,X1] :
( ~ relation(X2)
| apply(relation_dom_restriction(X2,X1),sK10(X1)) = apply(X2,sK10(X1))
| ~ function(X2)
| empty(X1) )
| ~ spl22_341 ),
inference(avatar_component_clause,[],[f3746]) ).
fof(f55161,plain,
( spl22_1415
| ~ spl22_145
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3200,f3185,f1312,f55159]) ).
fof(f55159,plain,
( spl22_1415
<=> ! [X16,X17] :
( ~ sP1(X16)
| sK13(X17,relation_rng(X16),relation_rng(X16)) = apply(X16,sK9(X16,sK13(X17,relation_rng(X16),relation_rng(X16))))
| sP2(X17,relation_rng(X16),relation_rng(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1415])]) ).
fof(f1312,plain,
( spl22_145
<=> ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_145])]) ).
fof(f3185,plain,
( spl22_299
<=> ! [X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_rng(X0))
| apply(X0,sK9(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_299])]) ).
fof(f3200,plain,
( ! [X16,X17] :
( ~ sP1(X16)
| sK13(X17,relation_rng(X16),relation_rng(X16)) = apply(X16,sK9(X16,sK13(X17,relation_rng(X16),relation_rng(X16))))
| sP2(X17,relation_rng(X16),relation_rng(X16)) )
| ~ spl22_145
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1313]) ).
fof(f1313,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_145 ),
inference(avatar_component_clause,[],[f1312]) ).
fof(f3186,plain,
( ! [X0,X1] :
( ~ in(X1,relation_rng(X0))
| ~ sP1(X0)
| apply(X0,sK9(X0,X1)) = X1 )
| ~ spl22_299 ),
inference(avatar_component_clause,[],[f3185]) ).
fof(f55157,plain,
( spl22_1414
| ~ spl22_146
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3199,f3185,f1316,f55155]) ).
fof(f55155,plain,
( spl22_1414
<=> ! [X14,X15] :
( ~ sP1(X14)
| sK13(relation_rng(X14),X15,relation_rng(X14)) = apply(X14,sK9(X14,sK13(relation_rng(X14),X15,relation_rng(X14))))
| sP2(relation_rng(X14),X15,relation_rng(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1414])]) ).
fof(f1316,plain,
( spl22_146
<=> ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_146])]) ).
fof(f3199,plain,
( ! [X14,X15] :
( ~ sP1(X14)
| sK13(relation_rng(X14),X15,relation_rng(X14)) = apply(X14,sK9(X14,sK13(relation_rng(X14),X15,relation_rng(X14))))
| sP2(relation_rng(X14),X15,relation_rng(X14)) )
| ~ spl22_146
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1317]) ).
fof(f1317,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl22_146 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f55153,plain,
( spl22_1413
| ~ spl22_79
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2506,f2439,f718,f55151]) ).
fof(f55151,plain,
( spl22_1413
<=> ! [X13,X14,X15] :
( in(sK7(X13,set_intersection2(X14,X15)),X14)
| sK7(X13,set_intersection2(X14,X15)) = apply(X13,sK8(X13,set_intersection2(X14,X15)))
| sP0(X13,set_intersection2(X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1413])]) ).
fof(f718,plain,
( spl22_79
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_79])]) ).
fof(f2506,plain,
( ! [X14,X15,X13] :
( in(sK7(X13,set_intersection2(X14,X15)),X14)
| sK7(X13,set_intersection2(X14,X15)) = apply(X13,sK8(X13,set_intersection2(X14,X15)))
| sP0(X13,set_intersection2(X14,X15)) )
| ~ spl22_79
| ~ spl22_238 ),
inference(resolution,[],[f2440,f719]) ).
fof(f719,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1) )
| ~ spl22_79 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f55149,plain,
( spl22_1412
| ~ spl22_79
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2475,f2435,f718,f55147]) ).
fof(f55147,plain,
( spl22_1412
<=> ! [X13,X14,X15] :
( in(sK7(X13,set_intersection2(X14,X15)),X15)
| sK7(X13,set_intersection2(X14,X15)) = apply(X13,sK8(X13,set_intersection2(X14,X15)))
| sP0(X13,set_intersection2(X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1412])]) ).
fof(f2475,plain,
( ! [X14,X15,X13] :
( in(sK7(X13,set_intersection2(X14,X15)),X15)
| sK7(X13,set_intersection2(X14,X15)) = apply(X13,sK8(X13,set_intersection2(X14,X15)))
| sP0(X13,set_intersection2(X14,X15)) )
| ~ spl22_79
| ~ spl22_237 ),
inference(resolution,[],[f2436,f719]) ).
fof(f55003,plain,
( spl22_1411
| ~ spl22_45
| ~ spl22_1399 ),
inference(avatar_split_clause,[],[f49312,f49021,f448,f55001]) ).
fof(f55001,plain,
( spl22_1411
<=> ! [X11] :
( sP0(X11,sK15)
| ~ in(relation_dom(X11),sK8(X11,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1411])]) ).
fof(f49021,plain,
( spl22_1399
<=> ! [X95] :
( sP0(X95,sK15)
| in(sK8(X95,sK15),relation_dom(X95)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1399])]) ).
fof(f49312,plain,
( ! [X11] :
( sP0(X11,sK15)
| ~ in(relation_dom(X11),sK8(X11,sK15)) )
| ~ spl22_45
| ~ spl22_1399 ),
inference(resolution,[],[f49022,f449]) ).
fof(f49022,plain,
( ! [X95] :
( in(sK8(X95,sK15),relation_dom(X95))
| sP0(X95,sK15) )
| ~ spl22_1399 ),
inference(avatar_component_clause,[],[f49021]) ).
fof(f51827,plain,
( spl22_1410
| ~ spl22_125
| ~ spl22_1409 ),
inference(avatar_split_clause,[],[f50700,f49854,f1107,f51825]) ).
fof(f51825,plain,
( spl22_1410
<=> ! [X18] :
( sP0(X18,sK15)
| ~ empty(relation_rng(X18))
| ~ sP1(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1410])]) ).
fof(f49854,plain,
( spl22_1409
<=> ! [X7,X8] :
( sP0(X7,sK15)
| ~ sP0(X7,X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1409])]) ).
fof(f50700,plain,
( ! [X18] :
( sP0(X18,sK15)
| ~ empty(relation_rng(X18))
| ~ sP1(X18) )
| ~ spl22_125
| ~ spl22_1409 ),
inference(resolution,[],[f49855,f1108]) ).
fof(f49855,plain,
( ! [X8,X7] :
( ~ sP0(X7,X8)
| sP0(X7,sK15)
| ~ empty(X8) )
| ~ spl22_1409 ),
inference(avatar_component_clause,[],[f49854]) ).
fof(f49856,plain,
( spl22_1409
| ~ spl22_250
| ~ spl22_1399 ),
inference(avatar_split_clause,[],[f49309,f49021,f2571,f49854]) ).
fof(f49309,plain,
( ! [X8,X7] :
( sP0(X7,sK15)
| ~ sP0(X7,X8)
| ~ empty(X8) )
| ~ spl22_250
| ~ spl22_1399 ),
inference(resolution,[],[f49022,f2572]) ).
fof(f49059,plain,
( spl22_1408
| ~ spl22_255
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5073,f4961,f2711,f49057]) ).
fof(f49057,plain,
( spl22_1408
<=> ! [X166,X167,X168] :
( sK7(X166,powerset(X167)) = apply(X166,sK8(X166,powerset(X167)))
| ~ empty(X167)
| sP0(X166,powerset(X167))
| sP2(sK15,X168,sK7(X166,powerset(X167))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1408])]) ).
fof(f2711,plain,
( spl22_255
<=> ! [X9,X8] :
( in(sK13(sK15,X8,X9),X9)
| sP2(sK15,X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_255])]) ).
fof(f4961,plain,
( spl22_395
<=> ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_395])]) ).
fof(f5073,plain,
( ! [X168,X166,X167] :
( sK7(X166,powerset(X167)) = apply(X166,sK8(X166,powerset(X167)))
| ~ empty(X167)
| sP0(X166,powerset(X167))
| sP2(sK15,X168,sK7(X166,powerset(X167))) )
| ~ spl22_255
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2712]) ).
fof(f2712,plain,
( ! [X8,X9] :
( in(sK13(sK15,X8,X9),X9)
| sP2(sK15,X8,X9) )
| ~ spl22_255 ),
inference(avatar_component_clause,[],[f2711]) ).
fof(f4962,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| sP0(X0,powerset(X1)) )
| ~ spl22_395 ),
inference(avatar_component_clause,[],[f4961]) ).
fof(f49055,plain,
( spl22_1407
| ~ spl22_254
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5068,f4961,f2707,f49053]) ).
fof(f49053,plain,
( spl22_1407
<=> ! [X149,X148,X147] :
( sK7(X147,powerset(X148)) = apply(X147,sK8(X147,powerset(X148)))
| ~ empty(X148)
| sP0(X147,powerset(X148))
| sP2(X149,sK15,sK7(X147,powerset(X148))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1407])]) ).
fof(f2707,plain,
( spl22_254
<=> ! [X6,X7] :
( in(sK13(X6,sK15,X7),X7)
| sP2(X6,sK15,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_254])]) ).
fof(f5068,plain,
( ! [X148,X149,X147] :
( sK7(X147,powerset(X148)) = apply(X147,sK8(X147,powerset(X148)))
| ~ empty(X148)
| sP0(X147,powerset(X148))
| sP2(X149,sK15,sK7(X147,powerset(X148))) )
| ~ spl22_254
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2708]) ).
fof(f2708,plain,
( ! [X6,X7] :
( in(sK13(X6,sK15,X7),X7)
| sP2(X6,sK15,X7) )
| ~ spl22_254 ),
inference(avatar_component_clause,[],[f2707]) ).
fof(f49051,plain,
( spl22_1406
| ~ spl22_253
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5063,f4961,f2703,f49049]) ).
fof(f49049,plain,
( spl22_1406
<=> ! [X130,X128,X129] :
( sK7(X128,powerset(X129)) = apply(X128,sK8(X128,powerset(X129)))
| ~ empty(X129)
| sP0(X128,powerset(X129))
| sP2(X130,sK7(X128,powerset(X129)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1406])]) ).
fof(f2703,plain,
( spl22_253
<=> ! [X4,X5] :
( in(sK13(X4,X5,sK15),X5)
| sP2(X4,X5,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_253])]) ).
fof(f5063,plain,
( ! [X130,X128,X129] :
( sK7(X128,powerset(X129)) = apply(X128,sK8(X128,powerset(X129)))
| ~ empty(X129)
| sP0(X128,powerset(X129))
| sP2(X130,sK7(X128,powerset(X129)),sK15) )
| ~ spl22_253
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2704]) ).
fof(f2704,plain,
( ! [X4,X5] :
( in(sK13(X4,X5,sK15),X5)
| sP2(X4,X5,sK15) )
| ~ spl22_253 ),
inference(avatar_component_clause,[],[f2703]) ).
fof(f49047,plain,
( spl22_1405
| ~ spl22_252
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5062,f4961,f2699,f49045]) ).
fof(f49045,plain,
( spl22_1405
<=> ! [X125,X126,X127] :
( sK7(X125,powerset(X126)) = apply(X125,sK8(X125,powerset(X126)))
| ~ empty(X126)
| sP0(X125,powerset(X126))
| sP2(sK7(X125,powerset(X126)),X127,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1405])]) ).
fof(f2699,plain,
( spl22_252
<=> ! [X2,X3] :
( in(sK13(X2,X3,sK15),X2)
| sP2(X2,X3,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_252])]) ).
fof(f5062,plain,
( ! [X126,X127,X125] :
( sK7(X125,powerset(X126)) = apply(X125,sK8(X125,powerset(X126)))
| ~ empty(X126)
| sP0(X125,powerset(X126))
| sP2(sK7(X125,powerset(X126)),X127,sK15) )
| ~ spl22_252
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2700]) ).
fof(f2700,plain,
( ! [X2,X3] :
( in(sK13(X2,X3,sK15),X2)
| sP2(X2,X3,sK15) )
| ~ spl22_252 ),
inference(avatar_component_clause,[],[f2699]) ).
fof(f49043,plain,
( spl22_1404
| ~ spl22_56
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4931,f4594,f540,f49041]) ).
fof(f49041,plain,
( spl22_1404
<=> ! [X13,X12,X11] :
( element(sK13(X11,X12,sK10(powerset(X13))),X11)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1404])]) ).
fof(f540,plain,
( spl22_56
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_56])]) ).
fof(f4931,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,X12,sK10(powerset(X13))),X11)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) )
| ~ spl22_56
| ~ spl22_388 ),
inference(resolution,[],[f4595,f541]) ).
fof(f541,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl22_56 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f49039,plain,
( spl22_1403
| ~ spl22_56
| ~ spl22_386 ),
inference(avatar_split_clause,[],[f4880,f4586,f540,f49037]) ).
fof(f49037,plain,
( spl22_1403
<=> ! [X13,X12,X11] :
( element(sK13(sK10(powerset(X11)),X12,X13),X13)
| sP2(sK10(powerset(X11)),X12,X13)
| empty(X11)
| in(sK13(sK10(powerset(X11)),X12,X13),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1403])]) ).
fof(f4880,plain,
( ! [X11,X12,X13] :
( element(sK13(sK10(powerset(X11)),X12,X13),X13)
| sP2(sK10(powerset(X11)),X12,X13)
| empty(X11)
| in(sK13(sK10(powerset(X11)),X12,X13),X11) )
| ~ spl22_56
| ~ spl22_386 ),
inference(resolution,[],[f4587,f541]) ).
fof(f49035,plain,
( spl22_1402
| ~ spl22_56
| ~ spl22_383 ),
inference(avatar_split_clause,[],[f4821,f4574,f540,f49033]) ).
fof(f49033,plain,
( spl22_1402
<=> ! [X13,X12,X11] :
( element(sK13(X11,X12,sK10(powerset(X13))),X12)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1402])]) ).
fof(f4821,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,X12,sK10(powerset(X13))),X12)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) )
| ~ spl22_56
| ~ spl22_383 ),
inference(resolution,[],[f4575,f541]) ).
fof(f49031,plain,
( spl22_1401
| ~ spl22_56
| ~ spl22_381 ),
inference(avatar_split_clause,[],[f4766,f4566,f540,f49029]) ).
fof(f49029,plain,
( spl22_1401
<=> ! [X13,X12,X11] :
( element(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13)
| empty(X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1401])]) ).
fof(f4766,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13)
| empty(X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X12) )
| ~ spl22_56
| ~ spl22_381 ),
inference(resolution,[],[f4567,f541]) ).
fof(f49027,plain,
( spl22_1400
| ~ spl22_56
| ~ spl22_379 ),
inference(avatar_split_clause,[],[f4687,f4558,f540,f49025]) ).
fof(f49025,plain,
( spl22_1400
<=> ! [X13,X12,X11] :
( in(sK13(sK10(powerset(X11)),X12,X13),X13)
| sP2(sK10(powerset(X11)),X12,X13)
| empty(X11)
| in(sK13(sK10(powerset(X11)),X12,X13),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1400])]) ).
fof(f4687,plain,
( ! [X11,X12,X13] :
( in(sK13(sK10(powerset(X11)),X12,X13),X13)
| sP2(sK10(powerset(X11)),X12,X13)
| empty(X11)
| in(sK13(sK10(powerset(X11)),X12,X13),X11) )
| ~ spl22_56
| ~ spl22_379 ),
inference(resolution,[],[f4559,f541]) ).
fof(f49023,plain,
( spl22_115
| spl22_1399
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(avatar_split_clause,[],[f25987,f25700,f20554,f15007,f944,f494,f49021,f956]) ).
fof(f956,plain,
( spl22_115
<=> ! [X7] : ~ empty(X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_115])]) ).
fof(f494,plain,
( spl22_51
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_51])]) ).
fof(f944,plain,
( spl22_112
<=> ! [X0] : sK15 = set_intersection2(sK15,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_112])]) ).
fof(f15007,plain,
( spl22_823
<=> ! [X11] : relation_dom(relation_dom_restriction(sK5,X11)) = set_intersection2(relation_dom(sK5),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_823])]) ).
fof(f20554,plain,
( spl22_960
<=> ! [X18,X17,X19] :
( ~ sP0(X17,X18)
| ~ empty(X18)
| in(sK8(X19,relation_dom(X17)),relation_dom(X19))
| sP0(X19,relation_dom(X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_960])]) ).
fof(f25700,plain,
( spl22_1042
<=> ! [X0] :
( sP0(relation_dom_restriction(sK5,sK15),X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1042])]) ).
fof(f25987,plain,
( ! [X94,X95] :
( sP0(X95,sK15)
| in(sK8(X95,sK15),relation_dom(X95))
| ~ empty(X94) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25986,f945]) ).
fof(f945,plain,
( ! [X0] : sK15 = set_intersection2(sK15,X0)
| ~ spl22_112 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f25986,plain,
( ! [X94,X95] :
( sP0(X95,set_intersection2(sK15,relation_dom(sK5)))
| in(sK8(X95,sK15),relation_dom(X95))
| ~ empty(X94) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25985,f495]) ).
fof(f495,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
| ~ spl22_51 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f25985,plain,
( ! [X94,X95] :
( sP0(X95,set_intersection2(relation_dom(sK5),sK15))
| in(sK8(X95,sK15),relation_dom(X95))
| ~ empty(X94) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25984,f15008]) ).
fof(f15008,plain,
( ! [X11] : relation_dom(relation_dom_restriction(sK5,X11)) = set_intersection2(relation_dom(sK5),X11)
| ~ spl22_823 ),
inference(avatar_component_clause,[],[f15007]) ).
fof(f25984,plain,
( ! [X94,X95] :
( in(sK8(X95,sK15),relation_dom(X95))
| ~ empty(X94)
| sP0(X95,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25983,f945]) ).
fof(f25983,plain,
( ! [X94,X95] :
( in(sK8(X95,set_intersection2(sK15,relation_dom(sK5))),relation_dom(X95))
| ~ empty(X94)
| sP0(X95,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_51
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25982,f495]) ).
fof(f25982,plain,
( ! [X94,X95] :
( in(sK8(X95,set_intersection2(relation_dom(sK5),sK15)),relation_dom(X95))
| ~ empty(X94)
| sP0(X95,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_823
| ~ spl22_960
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25824,f15008]) ).
fof(f25824,plain,
( ! [X94,X95] :
( ~ empty(X94)
| in(sK8(X95,relation_dom(relation_dom_restriction(sK5,sK15))),relation_dom(X95))
| sP0(X95,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_960
| ~ spl22_1042 ),
inference(duplicate_literal_removal,[],[f25780]) ).
fof(f25780,plain,
( ! [X94,X95] :
( ~ empty(X94)
| ~ empty(X94)
| in(sK8(X95,relation_dom(relation_dom_restriction(sK5,sK15))),relation_dom(X95))
| sP0(X95,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_960
| ~ spl22_1042 ),
inference(resolution,[],[f25701,f20555]) ).
fof(f20555,plain,
( ! [X18,X19,X17] :
( ~ sP0(X17,X18)
| ~ empty(X18)
| in(sK8(X19,relation_dom(X17)),relation_dom(X19))
| sP0(X19,relation_dom(X17)) )
| ~ spl22_960 ),
inference(avatar_component_clause,[],[f20554]) ).
fof(f25701,plain,
( ! [X0] :
( sP0(relation_dom_restriction(sK5,sK15),X0)
| ~ empty(X0) )
| ~ spl22_1042 ),
inference(avatar_component_clause,[],[f25700]) ).
fof(f49019,plain,
( spl22_1398
| ~ spl22_56
| ~ spl22_378 ),
inference(avatar_split_clause,[],[f4658,f4554,f540,f49017]) ).
fof(f49017,plain,
( spl22_1398
<=> ! [X13,X12,X11] :
( in(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13)
| empty(X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1398])]) ).
fof(f4658,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13)
| empty(X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X12) )
| ~ spl22_56
| ~ spl22_378 ),
inference(resolution,[],[f4555,f541]) ).
fof(f49015,plain,
( spl22_1397
| ~ spl22_56
| ~ spl22_377 ),
inference(avatar_split_clause,[],[f4629,f4550,f540,f49013]) ).
fof(f49013,plain,
( spl22_1397
<=> ! [X13,X12,X11] :
( in(sK13(X11,X12,sK10(powerset(X13))),X12)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1397])]) ).
fof(f4629,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,X12,sK10(powerset(X13))),X12)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) )
| ~ spl22_56
| ~ spl22_377 ),
inference(resolution,[],[f4551,f541]) ).
fof(f49011,plain,
( spl22_1396
| ~ spl22_56
| ~ spl22_376 ),
inference(avatar_split_clause,[],[f4600,f4546,f540,f49009]) ).
fof(f49009,plain,
( spl22_1396
<=> ! [X13,X12,X11] :
( in(sK13(X11,X12,sK10(powerset(X13))),X11)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1396])]) ).
fof(f4600,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,X12,sK10(powerset(X13))),X11)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) )
| ~ spl22_56
| ~ spl22_376 ),
inference(resolution,[],[f4547,f541]) ).
fof(f49007,plain,
( spl22_1395
| ~ spl22_156
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4474,f4164,f1407,f49005]) ).
fof(f49005,plain,
( spl22_1395
<=> ! [X108,X106,X107,X109,X110] :
( sP2(powerset(X106),X107,X108)
| ~ empty(X106)
| in(sK13(powerset(X106),X107,X108),X108)
| sP2(sK13(powerset(X106),X107,X108),X109,X110)
| ~ empty(X110) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1395])]) ).
fof(f1407,plain,
( spl22_156
<=> ! [X11,X12,X10] :
( in(sK13(X10,X11,X12),X10)
| sP2(X10,X11,X12)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_156])]) ).
fof(f4474,plain,
( ! [X108,X109,X106,X107,X110] :
( sP2(powerset(X106),X107,X108)
| ~ empty(X106)
| in(sK13(powerset(X106),X107,X108),X108)
| sP2(sK13(powerset(X106),X107,X108),X109,X110)
| ~ empty(X110) )
| ~ spl22_156
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1408]) ).
fof(f1408,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X10)
| sP2(X10,X11,X12)
| ~ empty(X12) )
| ~ spl22_156 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f49003,plain,
( spl22_1394
| ~ spl22_154
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4470,f4164,f1399,f49001]) ).
fof(f49001,plain,
( spl22_1394
<=> ! [X88,X87,X89,X90,X86] :
( sP2(powerset(X86),X87,X88)
| ~ empty(X86)
| in(sK13(powerset(X86),X87,X88),X88)
| sP2(X89,sK13(powerset(X86),X87,X88),X90)
| ~ empty(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1394])]) ).
fof(f1399,plain,
( spl22_154
<=> ! [X12,X11,X10] :
( in(sK13(X10,X11,X12),X11)
| sP2(X10,X11,X12)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_154])]) ).
fof(f4470,plain,
( ! [X90,X88,X86,X89,X87] :
( sP2(powerset(X86),X87,X88)
| ~ empty(X86)
| in(sK13(powerset(X86),X87,X88),X88)
| sP2(X89,sK13(powerset(X86),X87,X88),X90)
| ~ empty(X90) )
| ~ spl22_154
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1400]) ).
fof(f1400,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X11)
| sP2(X10,X11,X12)
| ~ empty(X12) )
| ~ spl22_154 ),
inference(avatar_component_clause,[],[f1399]) ).
fof(f48999,plain,
( spl22_1393
| ~ spl22_157
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4463,f4164,f1411,f48997]) ).
fof(f48997,plain,
( spl22_1393
<=> ! [X55,X51,X53,X54,X52] :
( sP2(powerset(X51),X52,X53)
| ~ empty(X51)
| in(sK13(powerset(X51),X52,X53),X53)
| sP2(X54,X55,sK13(powerset(X51),X52,X53))
| ~ empty(X54) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1393])]) ).
fof(f1411,plain,
( spl22_157
<=> ! [X11,X12,X10] :
( in(sK13(X10,X11,X12),X12)
| sP2(X10,X11,X12)
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_157])]) ).
fof(f4463,plain,
( ! [X51,X54,X55,X52,X53] :
( sP2(powerset(X51),X52,X53)
| ~ empty(X51)
| in(sK13(powerset(X51),X52,X53),X53)
| sP2(X54,X55,sK13(powerset(X51),X52,X53))
| ~ empty(X54) )
| ~ spl22_157
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1412]) ).
fof(f1412,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X12)
| sP2(X10,X11,X12)
| ~ empty(X10) )
| ~ spl22_157 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f48995,plain,
( spl22_1392
| ~ spl22_155
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4462,f4164,f1403,f48993]) ).
fof(f48993,plain,
( spl22_1392
<=> ! [X48,X47,X50,X49,X46] :
( sP2(powerset(X46),X47,X48)
| ~ empty(X46)
| in(sK13(powerset(X46),X47,X48),X48)
| sP2(X49,X50,sK13(powerset(X46),X47,X48))
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1392])]) ).
fof(f1403,plain,
( spl22_155
<=> ! [X11,X12,X10] :
( in(sK13(X10,X11,X12),X12)
| sP2(X10,X11,X12)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_155])]) ).
fof(f4462,plain,
( ! [X50,X48,X46,X49,X47] :
( sP2(powerset(X46),X47,X48)
| ~ empty(X46)
| in(sK13(powerset(X46),X47,X48),X48)
| sP2(X49,X50,sK13(powerset(X46),X47,X48))
| ~ empty(X50) )
| ~ spl22_155
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1404]) ).
fof(f1404,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X12)
| sP2(X10,X11,X12)
| ~ empty(X11) )
| ~ spl22_155 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f48991,plain,
( spl22_1391
| ~ spl22_149
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4454,f4164,f1362,f48989]) ).
fof(f48989,plain,
( spl22_1391
<=> ! [X13,X14,X16,X15] :
( sP2(powerset(X13),X14,X15)
| ~ empty(X13)
| in(sK13(powerset(X13),X14,X15),X15)
| sP0(X16,sK13(powerset(X13),X14,X15))
| ~ empty(relation_dom(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1391])]) ).
fof(f1362,plain,
( spl22_149
<=> ! [X4,X5] :
( in(sK7(X4,X5),X5)
| sP0(X4,X5)
| ~ empty(relation_dom(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_149])]) ).
fof(f4454,plain,
( ! [X16,X14,X15,X13] :
( sP2(powerset(X13),X14,X15)
| ~ empty(X13)
| in(sK13(powerset(X13),X14,X15),X15)
| sP0(X16,sK13(powerset(X13),X14,X15))
| ~ empty(relation_dom(X16)) )
| ~ spl22_149
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1363]) ).
fof(f1363,plain,
( ! [X4,X5] :
( in(sK7(X4,X5),X5)
| sP0(X4,X5)
| ~ empty(relation_dom(X4)) )
| ~ spl22_149 ),
inference(avatar_component_clause,[],[f1362]) ).
fof(f48987,plain,
( spl22_1390
| ~ spl22_156
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4423,f4156,f1407,f48985]) ).
fof(f48985,plain,
( spl22_1390
<=> ! [X108,X106,X107,X109,X110] :
( sP2(X106,X107,powerset(X108))
| ~ empty(X108)
| in(sK13(X106,X107,powerset(X108)),X106)
| sP2(sK13(X106,X107,powerset(X108)),X109,X110)
| ~ empty(X110) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1390])]) ).
fof(f4423,plain,
( ! [X108,X109,X106,X107,X110] :
( sP2(X106,X107,powerset(X108))
| ~ empty(X108)
| in(sK13(X106,X107,powerset(X108)),X106)
| sP2(sK13(X106,X107,powerset(X108)),X109,X110)
| ~ empty(X110) )
| ~ spl22_156
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1408]) ).
fof(f48983,plain,
( spl22_1389
| ~ spl22_154
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4419,f4156,f1399,f48981]) ).
fof(f48981,plain,
( spl22_1389
<=> ! [X88,X87,X89,X90,X86] :
( sP2(X86,X87,powerset(X88))
| ~ empty(X88)
| in(sK13(X86,X87,powerset(X88)),X86)
| sP2(X89,sK13(X86,X87,powerset(X88)),X90)
| ~ empty(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1389])]) ).
fof(f4419,plain,
( ! [X90,X88,X86,X89,X87] :
( sP2(X86,X87,powerset(X88))
| ~ empty(X88)
| in(sK13(X86,X87,powerset(X88)),X86)
| sP2(X89,sK13(X86,X87,powerset(X88)),X90)
| ~ empty(X90) )
| ~ spl22_154
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1400]) ).
fof(f48976,plain,
( spl22_1388
| ~ spl22_157
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4412,f4156,f1411,f48974]) ).
fof(f48974,plain,
( spl22_1388
<=> ! [X55,X51,X53,X54,X52] :
( sP2(X51,X52,powerset(X53))
| ~ empty(X53)
| in(sK13(X51,X52,powerset(X53)),X51)
| sP2(X54,X55,sK13(X51,X52,powerset(X53)))
| ~ empty(X54) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1388])]) ).
fof(f4412,plain,
( ! [X51,X54,X55,X52,X53] :
( sP2(X51,X52,powerset(X53))
| ~ empty(X53)
| in(sK13(X51,X52,powerset(X53)),X51)
| sP2(X54,X55,sK13(X51,X52,powerset(X53)))
| ~ empty(X54) )
| ~ spl22_157
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1412]) ).
fof(f48972,plain,
( spl22_1387
| ~ spl22_155
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4411,f4156,f1403,f48970]) ).
fof(f48970,plain,
( spl22_1387
<=> ! [X48,X47,X50,X49,X46] :
( sP2(X46,X47,powerset(X48))
| ~ empty(X48)
| in(sK13(X46,X47,powerset(X48)),X46)
| sP2(X49,X50,sK13(X46,X47,powerset(X48)))
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1387])]) ).
fof(f4411,plain,
( ! [X50,X48,X46,X49,X47] :
( sP2(X46,X47,powerset(X48))
| ~ empty(X48)
| in(sK13(X46,X47,powerset(X48)),X46)
| sP2(X49,X50,sK13(X46,X47,powerset(X48)))
| ~ empty(X50) )
| ~ spl22_155
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1404]) ).
fof(f48968,plain,
( spl22_1386
| ~ spl22_149
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4403,f4156,f1362,f48966]) ).
fof(f48966,plain,
( spl22_1386
<=> ! [X13,X14,X16,X15] :
( sP2(X13,X14,powerset(X15))
| ~ empty(X15)
| in(sK13(X13,X14,powerset(X15)),X13)
| sP0(X16,sK13(X13,X14,powerset(X15)))
| ~ empty(relation_dom(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1386])]) ).
fof(f4403,plain,
( ! [X16,X14,X15,X13] :
( sP2(X13,X14,powerset(X15))
| ~ empty(X15)
| in(sK13(X13,X14,powerset(X15)),X13)
| sP0(X16,sK13(X13,X14,powerset(X15)))
| ~ empty(relation_dom(X16)) )
| ~ spl22_149
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1363]) ).
fof(f48964,plain,
( spl22_1385
| ~ spl22_156
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4372,f4148,f1407,f48962]) ).
fof(f48962,plain,
( spl22_1385
<=> ! [X108,X106,X107,X109,X110] :
( sP2(X106,powerset(X107),X108)
| ~ empty(X107)
| in(sK13(X106,powerset(X107),X108),X108)
| sP2(sK13(X106,powerset(X107),X108),X109,X110)
| ~ empty(X110) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1385])]) ).
fof(f4372,plain,
( ! [X108,X109,X106,X107,X110] :
( sP2(X106,powerset(X107),X108)
| ~ empty(X107)
| in(sK13(X106,powerset(X107),X108),X108)
| sP2(sK13(X106,powerset(X107),X108),X109,X110)
| ~ empty(X110) )
| ~ spl22_156
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1408]) ).
fof(f48960,plain,
( spl22_1384
| ~ spl22_154
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4368,f4148,f1399,f48958]) ).
fof(f48958,plain,
( spl22_1384
<=> ! [X88,X87,X89,X90,X86] :
( sP2(X86,powerset(X87),X88)
| ~ empty(X87)
| in(sK13(X86,powerset(X87),X88),X88)
| sP2(X89,sK13(X86,powerset(X87),X88),X90)
| ~ empty(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1384])]) ).
fof(f4368,plain,
( ! [X90,X88,X86,X89,X87] :
( sP2(X86,powerset(X87),X88)
| ~ empty(X87)
| in(sK13(X86,powerset(X87),X88),X88)
| sP2(X89,sK13(X86,powerset(X87),X88),X90)
| ~ empty(X90) )
| ~ spl22_154
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1400]) ).
fof(f48956,plain,
( spl22_1383
| ~ spl22_157
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4361,f4148,f1411,f48954]) ).
fof(f48954,plain,
( spl22_1383
<=> ! [X55,X51,X53,X54,X52] :
( sP2(X51,powerset(X52),X53)
| ~ empty(X52)
| in(sK13(X51,powerset(X52),X53),X53)
| sP2(X54,X55,sK13(X51,powerset(X52),X53))
| ~ empty(X54) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1383])]) ).
fof(f4361,plain,
( ! [X51,X54,X55,X52,X53] :
( sP2(X51,powerset(X52),X53)
| ~ empty(X52)
| in(sK13(X51,powerset(X52),X53),X53)
| sP2(X54,X55,sK13(X51,powerset(X52),X53))
| ~ empty(X54) )
| ~ spl22_157
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1412]) ).
fof(f48952,plain,
( spl22_1382
| ~ spl22_155
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4360,f4148,f1403,f48950]) ).
fof(f48950,plain,
( spl22_1382
<=> ! [X48,X47,X50,X49,X46] :
( sP2(X46,powerset(X47),X48)
| ~ empty(X47)
| in(sK13(X46,powerset(X47),X48),X48)
| sP2(X49,X50,sK13(X46,powerset(X47),X48))
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1382])]) ).
fof(f4360,plain,
( ! [X50,X48,X46,X49,X47] :
( sP2(X46,powerset(X47),X48)
| ~ empty(X47)
| in(sK13(X46,powerset(X47),X48),X48)
| sP2(X49,X50,sK13(X46,powerset(X47),X48))
| ~ empty(X50) )
| ~ spl22_155
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1404]) ).
fof(f48948,plain,
( spl22_1381
| ~ spl22_149
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4352,f4148,f1362,f48946]) ).
fof(f48946,plain,
( spl22_1381
<=> ! [X13,X14,X16,X15] :
( sP2(X13,powerset(X14),X15)
| ~ empty(X14)
| in(sK13(X13,powerset(X14),X15),X15)
| sP0(X16,sK13(X13,powerset(X14),X15))
| ~ empty(relation_dom(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1381])]) ).
fof(f4352,plain,
( ! [X16,X14,X15,X13] :
( sP2(X13,powerset(X14),X15)
| ~ empty(X14)
| in(sK13(X13,powerset(X14),X15),X15)
| sP0(X16,sK13(X13,powerset(X14),X15))
| ~ empty(relation_dom(X16)) )
| ~ spl22_149
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1363]) ).
fof(f48944,plain,
( spl22_1380
| ~ spl22_156
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4321,f4139,f1407,f48942]) ).
fof(f48942,plain,
( spl22_1380
<=> ! [X108,X106,X107,X109,X110] :
( sP2(X106,X107,powerset(X108))
| ~ empty(X108)
| in(sK13(X106,X107,powerset(X108)),X107)
| sP2(sK13(X106,X107,powerset(X108)),X109,X110)
| ~ empty(X110) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1380])]) ).
fof(f4321,plain,
( ! [X108,X109,X106,X107,X110] :
( sP2(X106,X107,powerset(X108))
| ~ empty(X108)
| in(sK13(X106,X107,powerset(X108)),X107)
| sP2(sK13(X106,X107,powerset(X108)),X109,X110)
| ~ empty(X110) )
| ~ spl22_156
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1408]) ).
fof(f48940,plain,
( spl22_1379
| ~ spl22_154
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4317,f4139,f1399,f48938]) ).
fof(f48938,plain,
( spl22_1379
<=> ! [X88,X87,X89,X90,X86] :
( sP2(X86,X87,powerset(X88))
| ~ empty(X88)
| in(sK13(X86,X87,powerset(X88)),X87)
| sP2(X89,sK13(X86,X87,powerset(X88)),X90)
| ~ empty(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1379])]) ).
fof(f4317,plain,
( ! [X90,X88,X86,X89,X87] :
( sP2(X86,X87,powerset(X88))
| ~ empty(X88)
| in(sK13(X86,X87,powerset(X88)),X87)
| sP2(X89,sK13(X86,X87,powerset(X88)),X90)
| ~ empty(X90) )
| ~ spl22_154
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1400]) ).
fof(f48936,plain,
( spl22_115
| spl22_1378
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(avatar_split_clause,[],[f25981,f25700,f20550,f15007,f944,f494,f48934,f956]) ).
fof(f48934,plain,
( spl22_1378
<=> ! [X93] :
( sP0(X93,sK15)
| element(sK8(X93,sK15),relation_dom(X93)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1378])]) ).
fof(f20550,plain,
( spl22_959
<=> ! [X9,X8,X10] :
( ~ sP0(X8,X9)
| ~ empty(X9)
| element(sK8(X10,relation_dom(X8)),relation_dom(X10))
| sP0(X10,relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_959])]) ).
fof(f25981,plain,
( ! [X92,X93] :
( sP0(X93,sK15)
| element(sK8(X93,sK15),relation_dom(X93))
| ~ empty(X92) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25980,f945]) ).
fof(f25980,plain,
( ! [X92,X93] :
( sP0(X93,set_intersection2(sK15,relation_dom(sK5)))
| element(sK8(X93,sK15),relation_dom(X93))
| ~ empty(X92) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25979,f495]) ).
fof(f25979,plain,
( ! [X92,X93] :
( sP0(X93,set_intersection2(relation_dom(sK5),sK15))
| element(sK8(X93,sK15),relation_dom(X93))
| ~ empty(X92) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25978,f15008]) ).
fof(f25978,plain,
( ! [X92,X93] :
( element(sK8(X93,sK15),relation_dom(X93))
| ~ empty(X92)
| sP0(X93,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_51
| ~ spl22_112
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25977,f945]) ).
fof(f25977,plain,
( ! [X92,X93] :
( element(sK8(X93,set_intersection2(sK15,relation_dom(sK5))),relation_dom(X93))
| ~ empty(X92)
| sP0(X93,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_51
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25976,f495]) ).
fof(f25976,plain,
( ! [X92,X93] :
( element(sK8(X93,set_intersection2(relation_dom(sK5),sK15)),relation_dom(X93))
| ~ empty(X92)
| sP0(X93,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_823
| ~ spl22_959
| ~ spl22_1042 ),
inference(forward_demodulation,[],[f25825,f15008]) ).
fof(f25825,plain,
( ! [X92,X93] :
( ~ empty(X92)
| element(sK8(X93,relation_dom(relation_dom_restriction(sK5,sK15))),relation_dom(X93))
| sP0(X93,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_959
| ~ spl22_1042 ),
inference(duplicate_literal_removal,[],[f25779]) ).
fof(f25779,plain,
( ! [X92,X93] :
( ~ empty(X92)
| ~ empty(X92)
| element(sK8(X93,relation_dom(relation_dom_restriction(sK5,sK15))),relation_dom(X93))
| sP0(X93,relation_dom(relation_dom_restriction(sK5,sK15))) )
| ~ spl22_959
| ~ spl22_1042 ),
inference(resolution,[],[f25701,f20551]) ).
fof(f20551,plain,
( ! [X10,X8,X9] :
( ~ sP0(X8,X9)
| ~ empty(X9)
| element(sK8(X10,relation_dom(X8)),relation_dom(X10))
| sP0(X10,relation_dom(X8)) )
| ~ spl22_959 ),
inference(avatar_component_clause,[],[f20550]) ).
fof(f48932,plain,
( spl22_1377
| ~ spl22_157
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4310,f4139,f1411,f48930]) ).
fof(f48930,plain,
( spl22_1377
<=> ! [X55,X51,X53,X54,X52] :
( sP2(X51,X52,powerset(X53))
| ~ empty(X53)
| in(sK13(X51,X52,powerset(X53)),X52)
| sP2(X54,X55,sK13(X51,X52,powerset(X53)))
| ~ empty(X54) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1377])]) ).
fof(f4310,plain,
( ! [X51,X54,X55,X52,X53] :
( sP2(X51,X52,powerset(X53))
| ~ empty(X53)
| in(sK13(X51,X52,powerset(X53)),X52)
| sP2(X54,X55,sK13(X51,X52,powerset(X53)))
| ~ empty(X54) )
| ~ spl22_157
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1412]) ).
fof(f48928,plain,
( spl22_1376
| ~ spl22_155
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4309,f4139,f1403,f48926]) ).
fof(f48926,plain,
( spl22_1376
<=> ! [X48,X47,X50,X49,X46] :
( sP2(X46,X47,powerset(X48))
| ~ empty(X48)
| in(sK13(X46,X47,powerset(X48)),X47)
| sP2(X49,X50,sK13(X46,X47,powerset(X48)))
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1376])]) ).
fof(f4309,plain,
( ! [X50,X48,X46,X49,X47] :
( sP2(X46,X47,powerset(X48))
| ~ empty(X48)
| in(sK13(X46,X47,powerset(X48)),X47)
| sP2(X49,X50,sK13(X46,X47,powerset(X48)))
| ~ empty(X50) )
| ~ spl22_155
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1404]) ).
fof(f48924,plain,
( spl22_1375
| ~ spl22_149
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4301,f4139,f1362,f48922]) ).
fof(f48922,plain,
( spl22_1375
<=> ! [X13,X14,X16,X15] :
( sP2(X13,X14,powerset(X15))
| ~ empty(X15)
| in(sK13(X13,X14,powerset(X15)),X14)
| sP0(X16,sK13(X13,X14,powerset(X15)))
| ~ empty(relation_dom(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1375])]) ).
fof(f4301,plain,
( ! [X16,X14,X15,X13] :
( sP2(X13,X14,powerset(X15))
| ~ empty(X15)
| in(sK13(X13,X14,powerset(X15)),X14)
| sP0(X16,sK13(X13,X14,powerset(X15)))
| ~ empty(relation_dom(X16)) )
| ~ spl22_149
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1363]) ).
fof(f48920,plain,
( spl22_1374
| ~ spl22_37
| ~ spl22_366 ),
inference(avatar_split_clause,[],[f4281,f4135,f397,f48918]) ).
fof(f48918,plain,
( spl22_1374
<=> ! [X6,X5] :
( empty(X5)
| apply(relation_dom_restriction(relation_dom(X6),powerset(X5)),sK6(X5)) = apply(relation_dom(X6),sK6(X5))
| ~ function(relation_dom(X6))
| empty(powerset(X5))
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1374])]) ).
fof(f397,plain,
( spl22_37
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_37])]) ).
fof(f4135,plain,
( spl22_366
<=> ! [X2,X1] :
( empty(powerset(X1))
| empty(X1)
| apply(relation_dom_restriction(X2,powerset(X1)),sK6(X1)) = apply(X2,sK6(X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_366])]) ).
fof(f4281,plain,
( ! [X6,X5] :
( empty(X5)
| apply(relation_dom_restriction(relation_dom(X6),powerset(X5)),sK6(X5)) = apply(relation_dom(X6),sK6(X5))
| ~ function(relation_dom(X6))
| empty(powerset(X5))
| ~ empty(X6) )
| ~ spl22_37
| ~ spl22_366 ),
inference(resolution,[],[f4136,f398]) ).
fof(f398,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_37 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f4136,plain,
( ! [X2,X1] :
( ~ relation(X2)
| empty(X1)
| apply(relation_dom_restriction(X2,powerset(X1)),sK6(X1)) = apply(X2,sK6(X1))
| ~ function(X2)
| empty(powerset(X1)) )
| ~ spl22_366 ),
inference(avatar_component_clause,[],[f4135]) ).
fof(f48916,plain,
( spl22_1373
| ~ spl22_35
| ~ spl22_366 ),
inference(avatar_split_clause,[],[f4280,f4135,f389,f48914]) ).
fof(f48914,plain,
( spl22_1373
<=> ! [X4,X3] :
( empty(X3)
| apply(relation_dom_restriction(relation_rng(X4),powerset(X3)),sK6(X3)) = apply(relation_rng(X4),sK6(X3))
| ~ function(relation_rng(X4))
| empty(powerset(X3))
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1373])]) ).
fof(f389,plain,
( spl22_35
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_35])]) ).
fof(f4280,plain,
( ! [X3,X4] :
( empty(X3)
| apply(relation_dom_restriction(relation_rng(X4),powerset(X3)),sK6(X3)) = apply(relation_rng(X4),sK6(X3))
| ~ function(relation_rng(X4))
| empty(powerset(X3))
| ~ empty(X4) )
| ~ spl22_35
| ~ spl22_366 ),
inference(resolution,[],[f4136,f390]) ).
fof(f390,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_35 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f48912,plain,
( spl22_1372
| ~ spl22_141
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4015,f3873,f1277,f48910]) ).
fof(f48910,plain,
( spl22_1372
<=> ! [X45,X43,X44] :
( subset(sK13(powerset(X43),X44,sK6(X45)),X43)
| sP2(powerset(X43),X44,sK6(X45))
| element(sK13(powerset(X43),X44,sK6(X45)),X45)
| empty(X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1372])]) ).
fof(f1277,plain,
( spl22_141
<=> ! [X4,X3] :
( element(X3,X4)
| ~ in(X3,sK6(X4))
| empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_141])]) ).
fof(f4015,plain,
( ! [X44,X45,X43] :
( subset(sK13(powerset(X43),X44,sK6(X45)),X43)
| sP2(powerset(X43),X44,sK6(X45))
| element(sK13(powerset(X43),X44,sK6(X45)),X45)
| empty(X45) )
| ~ spl22_141
| ~ spl22_354 ),
inference(resolution,[],[f3874,f1278]) ).
fof(f1278,plain,
( ! [X3,X4] :
( ~ in(X3,sK6(X4))
| element(X3,X4)
| empty(X4) )
| ~ spl22_141 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f48908,plain,
( spl22_1371
| ~ spl22_141
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3993,f3869,f1277,f48906]) ).
fof(f48906,plain,
( spl22_1371
<=> ! [X44,X43,X42] :
( subset(sK13(sK6(X42),X43,powerset(X44)),X44)
| sP2(sK6(X42),X43,powerset(X44))
| element(sK13(sK6(X42),X43,powerset(X44)),X42)
| empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1371])]) ).
fof(f3993,plain,
( ! [X44,X42,X43] :
( subset(sK13(sK6(X42),X43,powerset(X44)),X44)
| sP2(sK6(X42),X43,powerset(X44))
| element(sK13(sK6(X42),X43,powerset(X44)),X42)
| empty(X42) )
| ~ spl22_141
| ~ spl22_353 ),
inference(resolution,[],[f3870,f1278]) ).
fof(f48904,plain,
( spl22_1370
| ~ spl22_141
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3971,f3865,f1277,f48902]) ).
fof(f48902,plain,
( spl22_1370
<=> ! [X45,X44,X43] :
( subset(sK13(X43,powerset(X44),sK6(X45)),X44)
| sP2(X43,powerset(X44),sK6(X45))
| element(sK13(X43,powerset(X44),sK6(X45)),X45)
| empty(X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1370])]) ).
fof(f3971,plain,
( ! [X44,X45,X43] :
( subset(sK13(X43,powerset(X44),sK6(X45)),X44)
| sP2(X43,powerset(X44),sK6(X45))
| element(sK13(X43,powerset(X44),sK6(X45)),X45)
| empty(X45) )
| ~ spl22_141
| ~ spl22_352 ),
inference(resolution,[],[f3866,f1278]) ).
fof(f48900,plain,
( spl22_1369
| ~ spl22_141
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3949,f3861,f1277,f48898]) ).
fof(f48898,plain,
( spl22_1369
<=> ! [X45,X44,X43] :
( subset(sK13(X43,sK6(X44),powerset(X45)),X45)
| sP2(X43,sK6(X44),powerset(X45))
| element(sK13(X43,sK6(X44),powerset(X45)),X44)
| empty(X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1369])]) ).
fof(f3949,plain,
( ! [X44,X45,X43] :
( subset(sK13(X43,sK6(X44),powerset(X45)),X45)
| sP2(X43,sK6(X44),powerset(X45))
| element(sK13(X43,sK6(X44),powerset(X45)),X44)
| empty(X44) )
| ~ spl22_141
| ~ spl22_351 ),
inference(resolution,[],[f3862,f1278]) ).
fof(f48896,plain,
( spl22_1368
| ~ spl22_315
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3928,f3857,f3327,f48894]) ).
fof(f48894,plain,
( spl22_1368
<=> ! [X115,X118,X117,X116] :
( sP0(X115,powerset(X116))
| ~ empty(X116)
| in(sK8(X115,powerset(X116)),relation_dom(X115))
| ~ empty(X117)
| sP2(sK10(powerset(X117)),X118,sK7(X115,powerset(X116))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1368])]) ).
fof(f3327,plain,
( spl22_315
<=> ! [X16,X14,X15] :
( ~ empty(X14)
| in(sK13(sK10(powerset(X14)),X15,X16),X16)
| sP2(sK10(powerset(X14)),X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_315])]) ).
fof(f3857,plain,
( spl22_350
<=> ! [X2,X0,X1] :
( in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_350])]) ).
fof(f3928,plain,
( ! [X118,X116,X117,X115] :
( sP0(X115,powerset(X116))
| ~ empty(X116)
| in(sK8(X115,powerset(X116)),relation_dom(X115))
| ~ empty(X117)
| sP2(sK10(powerset(X117)),X118,sK7(X115,powerset(X116))) )
| ~ spl22_315
| ~ spl22_350 ),
inference(resolution,[],[f3858,f3328]) ).
fof(f3328,plain,
( ! [X16,X14,X15] :
( in(sK13(sK10(powerset(X14)),X15,X16),X16)
| ~ empty(X14)
| sP2(sK10(powerset(X14)),X15,X16) )
| ~ spl22_315 ),
inference(avatar_component_clause,[],[f3327]) ).
fof(f3858,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK7(X0,powerset(X1)))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0)) )
| ~ spl22_350 ),
inference(avatar_component_clause,[],[f3857]) ).
fof(f48891,plain,
( spl22_1367
| spl22_115
| ~ spl22_783
| ~ spl22_1042 ),
inference(avatar_split_clause,[],[f25833,f25700,f13766,f956,f48889]) ).
fof(f48889,plain,
( spl22_1367
<=> ! [X57] :
( sP0(relation_dom_restriction(sK5,sK15),sK10(powerset(X57)))
| ~ empty(X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1367])]) ).
fof(f13766,plain,
( spl22_783
<=> ! [X4,X5,X3] :
( ~ empty(X3)
| sP0(X4,sK10(powerset(X3)))
| ~ sP0(X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_783])]) ).
fof(f25833,plain,
( ! [X56,X57] :
( ~ empty(X56)
| sP0(relation_dom_restriction(sK5,sK15),sK10(powerset(X57)))
| ~ empty(X57) )
| ~ spl22_783
| ~ spl22_1042 ),
inference(duplicate_literal_removal,[],[f25767]) ).
fof(f25767,plain,
( ! [X56,X57] :
( ~ empty(X56)
| sP0(relation_dom_restriction(sK5,sK15),sK10(powerset(X57)))
| ~ empty(X57)
| ~ empty(X56) )
| ~ spl22_783
| ~ spl22_1042 ),
inference(resolution,[],[f25701,f13767]) ).
fof(f13767,plain,
( ! [X3,X4,X5] :
( ~ sP0(X4,X5)
| sP0(X4,sK10(powerset(X3)))
| ~ empty(X3)
| ~ empty(X5) )
| ~ spl22_783 ),
inference(avatar_component_clause,[],[f13766]) ).
fof(f48887,plain,
( spl22_1366
| ~ spl22_314
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3926,f3857,f3323,f48885]) ).
fof(f48885,plain,
( spl22_1366
<=> ! [X109,X108,X110,X111] :
( sP0(X108,powerset(X109))
| ~ empty(X109)
| in(sK8(X108,powerset(X109)),relation_dom(X108))
| ~ empty(X110)
| sP2(X111,sK10(powerset(X110)),sK7(X108,powerset(X109))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1366])]) ).
fof(f3323,plain,
( spl22_314
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| in(sK13(X12,sK10(powerset(X11)),X13),X13)
| sP2(X12,sK10(powerset(X11)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_314])]) ).
fof(f3926,plain,
( ! [X111,X108,X109,X110] :
( sP0(X108,powerset(X109))
| ~ empty(X109)
| in(sK8(X108,powerset(X109)),relation_dom(X108))
| ~ empty(X110)
| sP2(X111,sK10(powerset(X110)),sK7(X108,powerset(X109))) )
| ~ spl22_314
| ~ spl22_350 ),
inference(resolution,[],[f3858,f3324]) ).
fof(f3324,plain,
( ! [X11,X12,X13] :
( in(sK13(X12,sK10(powerset(X11)),X13),X13)
| ~ empty(X11)
| sP2(X12,sK10(powerset(X11)),X13) )
| ~ spl22_314 ),
inference(avatar_component_clause,[],[f3323]) ).
fof(f48883,plain,
( spl22_1365
| ~ spl22_313
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3922,f3857,f3319,f48881]) ).
fof(f48881,plain,
( spl22_1365
<=> ! [X98,X96,X97,X95] :
( sP0(X95,powerset(X96))
| ~ empty(X96)
| in(sK8(X95,powerset(X96)),relation_dom(X95))
| ~ empty(X97)
| sP2(X98,sK7(X95,powerset(X96)),sK10(powerset(X97))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1365])]) ).
fof(f3319,plain,
( spl22_313
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| in(sK13(X9,X10,sK10(powerset(X8))),X10)
| sP2(X9,X10,sK10(powerset(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_313])]) ).
fof(f3922,plain,
( ! [X98,X96,X97,X95] :
( sP0(X95,powerset(X96))
| ~ empty(X96)
| in(sK8(X95,powerset(X96)),relation_dom(X95))
| ~ empty(X97)
| sP2(X98,sK7(X95,powerset(X96)),sK10(powerset(X97))) )
| ~ spl22_313
| ~ spl22_350 ),
inference(resolution,[],[f3858,f3320]) ).
fof(f3320,plain,
( ! [X10,X8,X9] :
( in(sK13(X9,X10,sK10(powerset(X8))),X10)
| ~ empty(X8)
| sP2(X9,X10,sK10(powerset(X8))) )
| ~ spl22_313 ),
inference(avatar_component_clause,[],[f3319]) ).
fof(f48879,plain,
( spl22_1364
| ~ spl22_312
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3921,f3857,f3315,f48877]) ).
fof(f48877,plain,
( spl22_1364
<=> ! [X94,X93,X91,X92] :
( sP0(X91,powerset(X92))
| ~ empty(X92)
| in(sK8(X91,powerset(X92)),relation_dom(X91))
| ~ empty(X93)
| sP2(sK7(X91,powerset(X92)),X94,sK10(powerset(X93))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1364])]) ).
fof(f3315,plain,
( spl22_312
<=> ! [X6,X5,X7] :
( ~ empty(X5)
| in(sK13(X6,X7,sK10(powerset(X5))),X6)
| sP2(X6,X7,sK10(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_312])]) ).
fof(f3921,plain,
( ! [X91,X94,X92,X93] :
( sP0(X91,powerset(X92))
| ~ empty(X92)
| in(sK8(X91,powerset(X92)),relation_dom(X91))
| ~ empty(X93)
| sP2(sK7(X91,powerset(X92)),X94,sK10(powerset(X93))) )
| ~ spl22_312
| ~ spl22_350 ),
inference(resolution,[],[f3858,f3316]) ).
fof(f3316,plain,
( ! [X6,X7,X5] :
( in(sK13(X6,X7,sK10(powerset(X5))),X6)
| ~ empty(X5)
| sP2(X6,X7,sK10(powerset(X5))) )
| ~ spl22_312 ),
inference(avatar_component_clause,[],[f3315]) ).
fof(f48875,plain,
( spl22_1363
| ~ spl22_65
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f3838,f3831,f610,f48873]) ).
fof(f48873,plain,
( spl22_1363
<=> ! [X2,X0,X1] :
( sP2(sK10(powerset(powerset(X0))),X1,sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X2,sK13(sK10(powerset(powerset(X0))),X1,sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1363])]) ).
fof(f3838,plain,
( ! [X2,X0,X1] :
( sP2(sK10(powerset(powerset(X0))),X1,sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X2,sK13(sK10(powerset(powerset(X0))),X1,sK10(powerset(powerset(X0))))) )
| ~ spl22_65
| ~ spl22_347 ),
inference(resolution,[],[f3832,f611]) ).
fof(f48871,plain,
( spl22_1362
| ~ spl22_65
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f3834,f3827,f610,f48869]) ).
fof(f48869,plain,
( spl22_1362
<=> ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(powerset(X1))),sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK10(powerset(powerset(X1))),sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1362])]) ).
fof(f3834,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK10(powerset(powerset(X1))),sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK10(powerset(powerset(X1))),sK10(powerset(powerset(X1))))) )
| ~ spl22_65
| ~ spl22_346 ),
inference(resolution,[],[f3828,f611]) ).
fof(f48867,plain,
( spl22_1361
| ~ spl22_67
| ~ spl22_318 ),
inference(avatar_split_clause,[],[f3598,f3339,f633,f48865]) ).
fof(f48865,plain,
( spl22_1361
<=> ! [X4,X5,X3] :
( sP2(sK6(powerset(X3)),X4,sK6(powerset(X3)))
| empty(powerset(X3))
| element(X5,X3)
| ~ in(X5,sK13(sK6(powerset(X3)),X4,sK6(powerset(X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1361])]) ).
fof(f3339,plain,
( spl22_318
<=> ! [X12,X11] :
( sP2(sK6(X11),X12,sK6(X11))
| element(sK13(sK6(X11),X12,sK6(X11)),X11)
| empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_318])]) ).
fof(f3598,plain,
( ! [X3,X4,X5] :
( sP2(sK6(powerset(X3)),X4,sK6(powerset(X3)))
| empty(powerset(X3))
| element(X5,X3)
| ~ in(X5,sK13(sK6(powerset(X3)),X4,sK6(powerset(X3)))) )
| ~ spl22_67
| ~ spl22_318 ),
inference(resolution,[],[f3340,f634]) ).
fof(f3340,plain,
( ! [X11,X12] :
( element(sK13(sK6(X11),X12,sK6(X11)),X11)
| sP2(sK6(X11),X12,sK6(X11))
| empty(X11) )
| ~ spl22_318 ),
inference(avatar_component_clause,[],[f3339]) ).
fof(f48863,plain,
( spl22_1360
| ~ spl22_67
| ~ spl22_316 ),
inference(avatar_split_clause,[],[f3542,f3331,f633,f48861]) ).
fof(f48861,plain,
( spl22_1360
<=> ! [X4,X5,X3] :
( sP2(X3,sK6(powerset(X4)),sK6(powerset(X4)))
| empty(powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(X3,sK6(powerset(X4)),sK6(powerset(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1360])]) ).
fof(f3331,plain,
( spl22_316
<=> ! [X11,X12] :
( sP2(X11,sK6(X12),sK6(X12))
| element(sK13(X11,sK6(X12),sK6(X12)),X12)
| empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_316])]) ).
fof(f3542,plain,
( ! [X3,X4,X5] :
( sP2(X3,sK6(powerset(X4)),sK6(powerset(X4)))
| empty(powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(X3,sK6(powerset(X4)),sK6(powerset(X4)))) )
| ~ spl22_67
| ~ spl22_316 ),
inference(resolution,[],[f3332,f634]) ).
fof(f3332,plain,
( ! [X11,X12] :
( element(sK13(X11,sK6(X12),sK6(X12)),X12)
| sP2(X11,sK6(X12),sK6(X12))
| empty(X12) )
| ~ spl22_316 ),
inference(avatar_component_clause,[],[f3331]) ).
fof(f48859,plain,
( spl22_1359
| ~ spl22_288
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3535,f3327,f3027,f48857]) ).
fof(f48857,plain,
( spl22_1359
<=> ! [X38,X41,X40,X39] :
( ~ empty(X38)
| sP2(sK10(powerset(X38)),X39,apply(X40,X41))
| ~ sP0(X40,sK13(sK10(powerset(X38)),X39,apply(X40,X41)))
| ~ in(X41,relation_dom(X40)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1359])]) ).
fof(f3027,plain,
( spl22_288
<=> ! [X12,X11,X10] :
( ~ in(X10,relation_dom(X11))
| ~ sP0(X11,X12)
| ~ in(X12,apply(X11,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_288])]) ).
fof(f3535,plain,
( ! [X40,X38,X41,X39] :
( ~ empty(X38)
| sP2(sK10(powerset(X38)),X39,apply(X40,X41))
| ~ sP0(X40,sK13(sK10(powerset(X38)),X39,apply(X40,X41)))
| ~ in(X41,relation_dom(X40)) )
| ~ spl22_288
| ~ spl22_315 ),
inference(resolution,[],[f3328,f3028]) ).
fof(f3028,plain,
( ! [X10,X11,X12] :
( ~ in(X12,apply(X11,X10))
| ~ sP0(X11,X12)
| ~ in(X10,relation_dom(X11)) )
| ~ spl22_288 ),
inference(avatar_component_clause,[],[f3027]) ).
fof(f48855,plain,
( spl22_1358
| ~ spl22_288
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3518,f3323,f3027,f48853]) ).
fof(f48853,plain,
( spl22_1358
<=> ! [X38,X41,X40,X39] :
( ~ empty(X38)
| sP2(X39,sK10(powerset(X38)),apply(X40,X41))
| ~ sP0(X40,sK13(X39,sK10(powerset(X38)),apply(X40,X41)))
| ~ in(X41,relation_dom(X40)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1358])]) ).
fof(f3518,plain,
( ! [X40,X38,X41,X39] :
( ~ empty(X38)
| sP2(X39,sK10(powerset(X38)),apply(X40,X41))
| ~ sP0(X40,sK13(X39,sK10(powerset(X38)),apply(X40,X41)))
| ~ in(X41,relation_dom(X40)) )
| ~ spl22_288
| ~ spl22_314 ),
inference(resolution,[],[f3324,f3028]) ).
fof(f48851,plain,
( spl22_1357
| ~ spl22_288
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3501,f3319,f3027,f48849]) ).
fof(f48849,plain,
( spl22_1357
<=> ! [X38,X40,X39,X37] :
( ~ empty(X37)
| sP2(X38,apply(X39,X40),sK10(powerset(X37)))
| ~ sP0(X39,sK13(X38,apply(X39,X40),sK10(powerset(X37))))
| ~ in(X40,relation_dom(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1357])]) ).
fof(f3501,plain,
( ! [X40,X38,X39,X37] :
( ~ empty(X37)
| sP2(X38,apply(X39,X40),sK10(powerset(X37)))
| ~ sP0(X39,sK13(X38,apply(X39,X40),sK10(powerset(X37))))
| ~ in(X40,relation_dom(X39)) )
| ~ spl22_288
| ~ spl22_313 ),
inference(resolution,[],[f3320,f3028]) ).
fof(f48833,plain,
( spl22_1356
| ~ spl22_288
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3467,f3315,f3027,f48831]) ).
fof(f48831,plain,
( spl22_1356
<=> ! [X38,X40,X39,X37] :
( ~ empty(X37)
| sP2(apply(X38,X39),X40,sK10(powerset(X37)))
| ~ sP0(X38,sK13(apply(X38,X39),X40,sK10(powerset(X37))))
| ~ in(X39,relation_dom(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1356])]) ).
fof(f3467,plain,
( ! [X40,X38,X39,X37] :
( ~ empty(X37)
| sP2(apply(X38,X39),X40,sK10(powerset(X37)))
| ~ sP0(X38,sK13(apply(X38,X39),X40,sK10(powerset(X37))))
| ~ in(X39,relation_dom(X38)) )
| ~ spl22_288
| ~ spl22_312 ),
inference(resolution,[],[f3316,f3028]) ).
fof(f48829,plain,
( spl22_1355
| ~ spl22_156
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3215,f3185,f1407,f48827]) ).
fof(f48827,plain,
( spl22_1355
<=> ! [X61,X60,X62] :
( ~ sP1(X60)
| sK13(relation_rng(X60),X61,X62) = apply(X60,sK9(X60,sK13(relation_rng(X60),X61,X62)))
| sP2(relation_rng(X60),X61,X62)
| ~ empty(X62) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1355])]) ).
fof(f3215,plain,
( ! [X62,X60,X61] :
( ~ sP1(X60)
| sK13(relation_rng(X60),X61,X62) = apply(X60,sK9(X60,sK13(relation_rng(X60),X61,X62)))
| sP2(relation_rng(X60),X61,X62)
| ~ empty(X62) )
| ~ spl22_156
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1408]) ).
fof(f48825,plain,
( spl22_1354
| ~ spl22_154
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3211,f3185,f1399,f48823]) ).
fof(f48823,plain,
( spl22_1354
<=> ! [X50,X48,X49] :
( ~ sP1(X48)
| sK13(X49,relation_rng(X48),X50) = apply(X48,sK9(X48,sK13(X49,relation_rng(X48),X50)))
| sP2(X49,relation_rng(X48),X50)
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1354])]) ).
fof(f3211,plain,
( ! [X50,X48,X49] :
( ~ sP1(X48)
| sK13(X49,relation_rng(X48),X50) = apply(X48,sK9(X48,sK13(X49,relation_rng(X48),X50)))
| sP2(X49,relation_rng(X48),X50)
| ~ empty(X50) )
| ~ spl22_154
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1400]) ).
fof(f48821,plain,
( spl22_1353
| ~ spl22_157
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3204,f3185,f1411,f48819]) ).
fof(f48819,plain,
( spl22_1353
<=> ! [X29,X27,X28] :
( ~ sP1(X27)
| sK13(X28,X29,relation_rng(X27)) = apply(X27,sK9(X27,sK13(X28,X29,relation_rng(X27))))
| sP2(X28,X29,relation_rng(X27))
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1353])]) ).
fof(f3204,plain,
( ! [X28,X29,X27] :
( ~ sP1(X27)
| sK13(X28,X29,relation_rng(X27)) = apply(X27,sK9(X27,sK13(X28,X29,relation_rng(X27))))
| sP2(X28,X29,relation_rng(X27))
| ~ empty(X28) )
| ~ spl22_157
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1412]) ).
fof(f48817,plain,
( spl22_1352
| ~ spl22_155
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3203,f3185,f1403,f48815]) ).
fof(f48815,plain,
( spl22_1352
<=> ! [X25,X24,X26] :
( ~ sP1(X24)
| sK13(X25,X26,relation_rng(X24)) = apply(X24,sK9(X24,sK13(X25,X26,relation_rng(X24))))
| sP2(X25,X26,relation_rng(X24))
| ~ empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1352])]) ).
fof(f3203,plain,
( ! [X26,X24,X25] :
( ~ sP1(X24)
| sK13(X25,X26,relation_rng(X24)) = apply(X24,sK9(X24,sK13(X25,X26,relation_rng(X24))))
| sP2(X25,X26,relation_rng(X24))
| ~ empty(X26) )
| ~ spl22_155
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1404]) ).
fof(f48813,plain,
( spl22_1351
| ~ spl22_159
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3113,f3027,f1481,f48811]) ).
fof(f48811,plain,
( spl22_1351
<=> ! [X9,X7,X8] :
( ~ sP0(X7,sK7(X8,apply(X7,X9)))
| ~ in(X9,relation_dom(X7))
| element(sK8(X8,apply(X7,X9)),relation_dom(X8))
| sP0(X8,apply(X7,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1351])]) ).
fof(f1481,plain,
( spl22_159
<=> ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| element(sK8(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_159])]) ).
fof(f3113,plain,
( ! [X8,X9,X7] :
( ~ sP0(X7,sK7(X8,apply(X7,X9)))
| ~ in(X9,relation_dom(X7))
| element(sK8(X8,apply(X7,X9)),relation_dom(X8))
| sP0(X8,apply(X7,X9)) )
| ~ spl22_159
| ~ spl22_288 ),
inference(resolution,[],[f3028,f1482]) ).
fof(f1482,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_159 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f48809,plain,
( spl22_1350
| ~ spl22_76
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3087,f3019,f684,f48807]) ).
fof(f48807,plain,
( spl22_1350
<=> ! [X12,X11,X10] :
( ~ in(X10,relation_rng(X11))
| ~ sP1(X11)
| apply(relation_dom_restriction(X12,relation_dom(X11)),sK9(X11,X10)) = apply(X12,sK9(X11,X10))
| ~ function(X12)
| ~ relation(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1350])]) ).
fof(f684,plain,
( spl22_76
<=> ! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_76])]) ).
fof(f3019,plain,
( spl22_286
<=> ! [X2,X3] :
( ~ sP1(X2)
| ~ in(X3,relation_rng(X2))
| in(sK9(X2,X3),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_286])]) ).
fof(f3087,plain,
( ! [X10,X11,X12] :
( ~ in(X10,relation_rng(X11))
| ~ sP1(X11)
| apply(relation_dom_restriction(X12,relation_dom(X11)),sK9(X11,X10)) = apply(X12,sK9(X11,X10))
| ~ function(X12)
| ~ relation(X12) )
| ~ spl22_76
| ~ spl22_286 ),
inference(resolution,[],[f3020,f685]) ).
fof(f685,plain,
( ! [X2,X0,X1] :
( ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_76 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f3020,plain,
( ! [X2,X3] :
( in(sK9(X2,X3),relation_dom(X2))
| ~ in(X3,relation_rng(X2))
| ~ sP1(X2) )
| ~ spl22_286 ),
inference(avatar_component_clause,[],[f3019]) ).
fof(f47824,plain,
( spl22_1349
| ~ spl22_236
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5165,f5153,f2331,f47822]) ).
fof(f47822,plain,
( spl22_1349
<=> ! [X24,X23] :
( sP0(X23,relation_dom(X24))
| apply(relation_dom_restriction(sK15,relation_dom(X23)),sK8(X23,relation_dom(X24))) = apply(sK15,sK8(X23,relation_dom(X24)))
| ~ sP0(X24,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1349])]) ).
fof(f5165,plain,
( ! [X24,X23] :
( sP0(X23,relation_dom(X24))
| apply(relation_dom_restriction(sK15,relation_dom(X23)),sK8(X23,relation_dom(X24))) = apply(sK15,sK8(X23,relation_dom(X24)))
| ~ sP0(X24,sK15) )
| ~ spl22_236
| ~ spl22_401 ),
inference(resolution,[],[f5154,f2332]) ).
fof(f47820,plain,
( spl22_1348
| ~ spl22_236
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5135,f5123,f2331,f47818]) ).
fof(f47818,plain,
( spl22_1348
<=> ! [X24,X23] :
( sP0(X23,relation_dom(X24))
| apply(relation_dom_restriction(sK20,relation_dom(X23)),sK8(X23,relation_dom(X24))) = apply(sK20,sK8(X23,relation_dom(X24)))
| ~ sP0(X24,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1348])]) ).
fof(f5135,plain,
( ! [X24,X23] :
( sP0(X23,relation_dom(X24))
| apply(relation_dom_restriction(sK20,relation_dom(X23)),sK8(X23,relation_dom(X24))) = apply(sK20,sK8(X23,relation_dom(X24)))
| ~ sP0(X24,sK15) )
| ~ spl22_236
| ~ spl22_400 ),
inference(resolution,[],[f5124,f2332]) ).
fof(f47816,plain,
( spl22_1347
| ~ spl22_236
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5105,f5093,f2331,f47814]) ).
fof(f47814,plain,
( spl22_1347
<=> ! [X24,X23] :
( sP0(X23,relation_dom(X24))
| apply(relation_dom_restriction(sK19,relation_dom(X23)),sK8(X23,relation_dom(X24))) = apply(sK19,sK8(X23,relation_dom(X24)))
| ~ sP0(X24,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1347])]) ).
fof(f5105,plain,
( ! [X24,X23] :
( sP0(X23,relation_dom(X24))
| apply(relation_dom_restriction(sK19,relation_dom(X23)),sK8(X23,relation_dom(X24))) = apply(sK19,sK8(X23,relation_dom(X24)))
| ~ sP0(X24,sK15) )
| ~ spl22_236
| ~ spl22_399 ),
inference(resolution,[],[f5094,f2332]) ).
fof(f47796,plain,
( spl22_1346
| ~ spl22_56
| ~ spl22_390 ),
inference(avatar_split_clause,[],[f4968,f4938,f540,f47794]) ).
fof(f47794,plain,
( spl22_1346
<=> ! [X9,X8] :
( empty(X8)
| sK7(X9,sK6(X8)) = apply(X9,sK8(X9,sK6(X8)))
| sP0(X9,sK6(X8))
| in(sK7(X9,sK6(X8)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1346])]) ).
fof(f4938,plain,
( spl22_390
<=> ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sK7(X0,sK6(X1)) = apply(X0,sK8(X0,sK6(X1)))
| sP0(X0,sK6(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_390])]) ).
fof(f4968,plain,
( ! [X8,X9] :
( empty(X8)
| sK7(X9,sK6(X8)) = apply(X9,sK8(X9,sK6(X8)))
| sP0(X9,sK6(X8))
| in(sK7(X9,sK6(X8)),X8) )
| ~ spl22_56
| ~ spl22_390 ),
inference(duplicate_literal_removal,[],[f4967]) ).
fof(f4967,plain,
( ! [X8,X9] :
( empty(X8)
| sK7(X9,sK6(X8)) = apply(X9,sK8(X9,sK6(X8)))
| sP0(X9,sK6(X8))
| empty(X8)
| in(sK7(X9,sK6(X8)),X8) )
| ~ spl22_56
| ~ spl22_390 ),
inference(resolution,[],[f4939,f541]) ).
fof(f4939,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sK7(X0,sK6(X1)) = apply(X0,sK8(X0,sK6(X1)))
| sP0(X0,sK6(X1)) )
| ~ spl22_390 ),
inference(avatar_component_clause,[],[f4938]) ).
fof(f47792,plain,
( spl22_1345
| ~ spl22_124
| ~ spl22_360 ),
inference(avatar_split_clause,[],[f4087,f4039,f1103,f47790]) ).
fof(f47790,plain,
( spl22_1345
<=> ! [X20,X19] :
( sP0(X19,powerset(X20))
| element(sK10(sK7(X19,powerset(X20))),X20)
| in(sK8(X19,powerset(X20)),relation_dom(X19))
| empty(sK7(X19,powerset(X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1345])]) ).
fof(f1103,plain,
( spl22_124
<=> ! [X3] :
( empty(X3)
| in(sK10(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_124])]) ).
fof(f4039,plain,
( spl22_360
<=> ! [X4,X5,X3] :
( in(sK8(X3,powerset(X4)),relation_dom(X3))
| sP0(X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_360])]) ).
fof(f4087,plain,
( ! [X19,X20] :
( sP0(X19,powerset(X20))
| element(sK10(sK7(X19,powerset(X20))),X20)
| in(sK8(X19,powerset(X20)),relation_dom(X19))
| empty(sK7(X19,powerset(X20))) )
| ~ spl22_124
| ~ spl22_360 ),
inference(resolution,[],[f4040,f1104]) ).
fof(f1104,plain,
( ! [X3] :
( in(sK10(X3),X3)
| empty(X3) )
| ~ spl22_124 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f4040,plain,
( ! [X3,X4,X5] :
( ~ in(X5,sK7(X3,powerset(X4)))
| sP0(X3,powerset(X4))
| element(X5,X4)
| in(sK8(X3,powerset(X4)),relation_dom(X3)) )
| ~ spl22_360 ),
inference(avatar_component_clause,[],[f4039]) ).
fof(f47788,plain,
( spl22_1344
| ~ spl22_52
| ~ spl22_359 ),
inference(avatar_split_clause,[],[f4078,f4035,f498,f47786]) ).
fof(f47786,plain,
( spl22_1344
<=> ! [X6,X7] :
( element(sK8(X6,sK10(powerset(powerset(X7)))),relation_dom(X6))
| sP0(X6,sK10(powerset(powerset(X7))))
| subset(sK7(X6,sK10(powerset(powerset(X7)))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1344])]) ).
fof(f4078,plain,
( ! [X6,X7] :
( element(sK8(X6,sK10(powerset(powerset(X7)))),relation_dom(X6))
| sP0(X6,sK10(powerset(powerset(X7))))
| subset(sK7(X6,sK10(powerset(powerset(X7)))),X7) )
| ~ spl22_52
| ~ spl22_359 ),
inference(resolution,[],[f4036,f499]) ).
fof(f47784,plain,
( spl22_1343
| ~ spl22_52
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4063,f4027,f498,f47782]) ).
fof(f47782,plain,
( spl22_1343
<=> ! [X6,X7] :
( in(sK8(X6,sK10(powerset(powerset(X7)))),relation_dom(X6))
| sP0(X6,sK10(powerset(powerset(X7))))
| subset(sK7(X6,sK10(powerset(powerset(X7)))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1343])]) ).
fof(f4063,plain,
( ! [X6,X7] :
( in(sK8(X6,sK10(powerset(powerset(X7)))),relation_dom(X6))
| sP0(X6,sK10(powerset(powerset(X7))))
| subset(sK7(X6,sK10(powerset(powerset(X7)))),X7) )
| ~ spl22_52
| ~ spl22_357 ),
inference(resolution,[],[f4028,f499]) ).
fof(f47780,plain,
( spl22_1342
| ~ spl22_62
| ~ spl22_356 ),
inference(avatar_split_clause,[],[f4046,f4023,f598,f47778]) ).
fof(f47778,plain,
( spl22_1342
<=> ! [X13,X12] :
( sK7(X12,sK10(powerset(X13))) = apply(X12,sK8(X12,sK10(powerset(X13))))
| ~ empty(X13)
| sK10(powerset(X13)) = relation_rng(X12)
| ~ sP1(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1342])]) ).
fof(f598,plain,
( spl22_62
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_62])]) ).
fof(f4023,plain,
( spl22_356
<=> ! [X0,X1] :
( ~ empty(X0)
| sK7(X1,sK10(powerset(X0))) = apply(X1,sK8(X1,sK10(powerset(X0))))
| sP0(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_356])]) ).
fof(f4046,plain,
( ! [X12,X13] :
( sK7(X12,sK10(powerset(X13))) = apply(X12,sK8(X12,sK10(powerset(X13))))
| ~ empty(X13)
| sK10(powerset(X13)) = relation_rng(X12)
| ~ sP1(X12) )
| ~ spl22_62
| ~ spl22_356 ),
inference(resolution,[],[f4024,f599]) ).
fof(f599,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1)
| relation_rng(X0) = X1
| ~ sP1(X0) )
| ~ spl22_62 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f4024,plain,
( ! [X0,X1] :
( sP0(X1,sK10(powerset(X0)))
| sK7(X1,sK10(powerset(X0))) = apply(X1,sK8(X1,sK10(powerset(X0))))
| ~ empty(X0) )
| ~ spl22_356 ),
inference(avatar_component_clause,[],[f4023]) ).
fof(f47776,plain,
( spl22_1341
| ~ spl22_145
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3904,f3857,f1312,f47774]) ).
fof(f47774,plain,
( spl22_1341
<=> ! [X25,X24,X26] :
( sP0(X24,powerset(X25))
| ~ empty(X25)
| in(sK8(X24,powerset(X25)),relation_dom(X24))
| sP2(X26,sK7(X24,powerset(X25)),sK7(X24,powerset(X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1341])]) ).
fof(f3904,plain,
( ! [X26,X24,X25] :
( sP0(X24,powerset(X25))
| ~ empty(X25)
| in(sK8(X24,powerset(X25)),relation_dom(X24))
| sP2(X26,sK7(X24,powerset(X25)),sK7(X24,powerset(X25))) )
| ~ spl22_145
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1313]) ).
fof(f47772,plain,
( spl22_1340
| ~ spl22_146
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3903,f3857,f1316,f47770]) ).
fof(f47770,plain,
( spl22_1340
<=> ! [X22,X21,X23] :
( sP0(X21,powerset(X22))
| ~ empty(X22)
| in(sK8(X21,powerset(X22)),relation_dom(X21))
| sP2(sK7(X21,powerset(X22)),X23,sK7(X21,powerset(X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1340])]) ).
fof(f3903,plain,
( ! [X21,X22,X23] :
( sP0(X21,powerset(X22))
| ~ empty(X22)
| in(sK8(X21,powerset(X22)),relation_dom(X21))
| sP2(sK7(X21,powerset(X22)),X23,sK7(X21,powerset(X22))) )
| ~ spl22_146
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1317]) ).
fof(f47768,plain,
( spl22_1339
| ~ spl22_153
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3896,f3857,f1395,f47766]) ).
fof(f47766,plain,
( spl22_1339
<=> ! [X0,X3,X2,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1339])]) ).
fof(f3896,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,powerset(X1))
| ~ empty(X1)
| in(sK8(X0,powerset(X1)),relation_dom(X0))
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,sK7(X0,powerset(X1))) )
| ~ spl22_153
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1396]) ).
fof(f47764,plain,
( spl22_1338
| ~ spl22_52
| ~ spl22_349 ),
inference(avatar_split_clause,[],[f3892,f3853,f498,f47762]) ).
fof(f47762,plain,
( spl22_1338
<=> ! [X6,X7] :
( element(sK8(X6,sK6(powerset(X7))),relation_dom(X6))
| sP0(X6,sK6(powerset(X7)))
| empty(powerset(X7))
| subset(sK7(X6,sK6(powerset(X7))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1338])]) ).
fof(f3892,plain,
( ! [X6,X7] :
( element(sK8(X6,sK6(powerset(X7))),relation_dom(X6))
| sP0(X6,sK6(powerset(X7)))
| empty(powerset(X7))
| subset(sK7(X6,sK6(powerset(X7))),X7) )
| ~ spl22_52
| ~ spl22_349 ),
inference(resolution,[],[f3854,f499]) ).
fof(f47760,plain,
( spl22_1337
| ~ spl22_52
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3885,f3849,f498,f47758]) ).
fof(f47758,plain,
( spl22_1337
<=> ! [X6,X7] :
( in(sK8(X6,sK6(powerset(X7))),relation_dom(X6))
| empty(powerset(X7))
| sP0(X6,sK6(powerset(X7)))
| subset(sK7(X6,sK6(powerset(X7))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1337])]) ).
fof(f3885,plain,
( ! [X6,X7] :
( in(sK8(X6,sK6(powerset(X7))),relation_dom(X6))
| empty(powerset(X7))
| sP0(X6,sK6(powerset(X7)))
| subset(sK7(X6,sK6(powerset(X7))),X7) )
| ~ spl22_52
| ~ spl22_348 ),
inference(resolution,[],[f3850,f499]) ).
fof(f47756,plain,
( spl22_1336
| ~ spl22_513
| ~ spl22_1271 ),
inference(avatar_split_clause,[],[f39905,f39711,f7070,f47754]) ).
fof(f47754,plain,
( spl22_1336
<=> ! [X9] :
( ~ sP0(relation_dom_restriction(sK5,X9),sK15)
| ~ sP0(sK5,set_intersection2(X9,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1336])]) ).
fof(f7070,plain,
( spl22_513
<=> ! [X0] :
( ~ sP0(sK5,X0)
| in(apply(sK5,sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_513])]) ).
fof(f39711,plain,
( spl22_1271
<=> ! [X2,X1] :
( ~ in(X2,set_intersection2(X1,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X1),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1271])]) ).
fof(f39905,plain,
( ! [X9] :
( ~ sP0(relation_dom_restriction(sK5,X9),sK15)
| ~ sP0(sK5,set_intersection2(X9,relation_dom(sK5))) )
| ~ spl22_513
| ~ spl22_1271 ),
inference(resolution,[],[f39712,f7071]) ).
fof(f7071,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(sK5,X0) )
| ~ spl22_513 ),
inference(avatar_component_clause,[],[f7070]) ).
fof(f39712,plain,
( ! [X2,X1] :
( ~ in(X2,set_intersection2(X1,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X1),sK15) )
| ~ spl22_1271 ),
inference(avatar_component_clause,[],[f39711]) ).
fof(f47752,plain,
( spl22_1335
| ~ spl22_44
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3788,f3750,f444,f47750]) ).
fof(f47750,plain,
( spl22_1335
<=> ! [X9,X8,X7] :
( apply(relation_dom_restriction(relation_dom_restriction(X7,X8),powerset(X9)),sK15) = apply(relation_dom_restriction(X7,X8),sK15)
| ~ function(relation_dom_restriction(X7,X8))
| empty(powerset(X9))
| ~ relation(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1335])]) ).
fof(f444,plain,
( spl22_44
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_44])]) ).
fof(f3788,plain,
( ! [X8,X9,X7] :
( apply(relation_dom_restriction(relation_dom_restriction(X7,X8),powerset(X9)),sK15) = apply(relation_dom_restriction(X7,X8),sK15)
| ~ function(relation_dom_restriction(X7,X8))
| empty(powerset(X9))
| ~ relation(X7) )
| ~ spl22_44
| ~ spl22_342 ),
inference(resolution,[],[f3751,f445]) ).
fof(f445,plain,
( ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) )
| ~ spl22_44 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f47748,plain,
( spl22_1334
| ~ spl22_44
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3769,f3746,f444,f47746]) ).
fof(f47746,plain,
( spl22_1334
<=> ! [X9,X8,X7] :
( apply(relation_dom_restriction(relation_dom_restriction(X7,X8),X9),sK10(X9)) = apply(relation_dom_restriction(X7,X8),sK10(X9))
| ~ function(relation_dom_restriction(X7,X8))
| empty(X9)
| ~ relation(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1334])]) ).
fof(f3769,plain,
( ! [X8,X9,X7] :
( apply(relation_dom_restriction(relation_dom_restriction(X7,X8),X9),sK10(X9)) = apply(relation_dom_restriction(X7,X8),sK10(X9))
| ~ function(relation_dom_restriction(X7,X8))
| empty(X9)
| ~ relation(X7) )
| ~ spl22_44
| ~ spl22_341 ),
inference(resolution,[],[f3747,f445]) ).
fof(f47744,plain,
( spl22_1333
| ~ spl22_65
| ~ spl22_318 ),
inference(avatar_split_clause,[],[f3597,f3339,f610,f47742]) ).
fof(f47742,plain,
( spl22_1333
<=> ! [X2,X0,X1] :
( sP2(sK6(powerset(X0)),X1,sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X2,sK13(sK6(powerset(X0)),X1,sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1333])]) ).
fof(f3597,plain,
( ! [X2,X0,X1] :
( sP2(sK6(powerset(X0)),X1,sK6(powerset(X0)))
| empty(powerset(X0))
| ~ empty(X0)
| ~ in(X2,sK13(sK6(powerset(X0)),X1,sK6(powerset(X0)))) )
| ~ spl22_65
| ~ spl22_318 ),
inference(resolution,[],[f3340,f611]) ).
fof(f47740,plain,
( spl22_1332
| ~ spl22_65
| ~ spl22_316 ),
inference(avatar_split_clause,[],[f3541,f3331,f610,f47738]) ).
fof(f47738,plain,
( spl22_1332
<=> ! [X2,X0,X1] :
( sP2(X0,sK6(powerset(X1)),sK6(powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK6(powerset(X1)),sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1332])]) ).
fof(f3541,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK6(powerset(X1)),sK6(powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK6(powerset(X1)),sK6(powerset(X1)))) )
| ~ spl22_65
| ~ spl22_316 ),
inference(resolution,[],[f3332,f611]) ).
fof(f47736,plain,
( spl22_1331
| ~ spl22_76
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2854,f2711,f684,f47734]) ).
fof(f47734,plain,
( spl22_1331
<=> ! [X6,X4,X5] :
( sP2(sK15,X4,X5)
| apply(relation_dom_restriction(X6,X5),sK13(sK15,X4,X5)) = apply(X6,sK13(sK15,X4,X5))
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1331])]) ).
fof(f2854,plain,
( ! [X6,X4,X5] :
( sP2(sK15,X4,X5)
| apply(relation_dom_restriction(X6,X5),sK13(sK15,X4,X5)) = apply(X6,sK13(sK15,X4,X5))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_76
| ~ spl22_255 ),
inference(resolution,[],[f2712,f685]) ).
fof(f47732,plain,
( spl22_1330
| ~ spl22_76
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2839,f2707,f684,f47730]) ).
fof(f47730,plain,
( spl22_1330
<=> ! [X6,X4,X5] :
( sP2(X4,sK15,X5)
| apply(relation_dom_restriction(X6,X5),sK13(X4,sK15,X5)) = apply(X6,sK13(X4,sK15,X5))
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1330])]) ).
fof(f2839,plain,
( ! [X6,X4,X5] :
( sP2(X4,sK15,X5)
| apply(relation_dom_restriction(X6,X5),sK13(X4,sK15,X5)) = apply(X6,sK13(X4,sK15,X5))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_76
| ~ spl22_254 ),
inference(resolution,[],[f2708,f685]) ).
fof(f47728,plain,
( spl22_1329
| ~ spl22_76
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2819,f2703,f684,f47726]) ).
fof(f47726,plain,
( spl22_1329
<=> ! [X4,X5,X3] :
( sP2(X3,X4,sK15)
| apply(X5,sK13(X3,X4,sK15)) = apply(relation_dom_restriction(X5,X4),sK13(X3,X4,sK15))
| ~ function(X5)
| ~ relation(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1329])]) ).
fof(f2819,plain,
( ! [X3,X4,X5] :
( sP2(X3,X4,sK15)
| apply(X5,sK13(X3,X4,sK15)) = apply(relation_dom_restriction(X5,X4),sK13(X3,X4,sK15))
| ~ function(X5)
| ~ relation(X5) )
| ~ spl22_76
| ~ spl22_253 ),
inference(resolution,[],[f2704,f685]) ).
fof(f47724,plain,
( spl22_1328
| ~ spl22_76
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2804,f2699,f684,f47722]) ).
fof(f47722,plain,
( spl22_1328
<=> ! [X4,X5,X3] :
( sP2(X3,X4,sK15)
| apply(relation_dom_restriction(X5,X3),sK13(X3,X4,sK15)) = apply(X5,sK13(X3,X4,sK15))
| ~ function(X5)
| ~ relation(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1328])]) ).
fof(f2804,plain,
( ! [X3,X4,X5] :
( sP2(X3,X4,sK15)
| apply(relation_dom_restriction(X5,X3),sK13(X3,X4,sK15)) = apply(X5,sK13(X3,X4,sK15))
| ~ function(X5)
| ~ relation(X5) )
| ~ spl22_76
| ~ spl22_252 ),
inference(resolution,[],[f2700,f685]) ).
fof(f47715,plain,
( spl22_1327
| ~ spl22_119
| ~ spl22_961 ),
inference(avatar_split_clause,[],[f22917,f20558,f1078,f47713]) ).
fof(f47713,plain,
( spl22_1327
<=> ! [X8] :
( ~ empty(relation_dom_restriction(sK5,X8))
| sK15 = relation_dom(set_intersection2(X8,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1327])]) ).
fof(f1078,plain,
( spl22_119
<=> ! [X0] :
( relation_dom(X0) = sK15
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_119])]) ).
fof(f20558,plain,
( spl22_961
<=> ! [X0] :
( empty(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_961])]) ).
fof(f22917,plain,
( ! [X8] :
( ~ empty(relation_dom_restriction(sK5,X8))
| sK15 = relation_dom(set_intersection2(X8,relation_dom(sK5))) )
| ~ spl22_119
| ~ spl22_961 ),
inference(resolution,[],[f20559,f1079]) ).
fof(f1079,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK15 )
| ~ spl22_119 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f20559,plain,
( ! [X0] :
( empty(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_961 ),
inference(avatar_component_clause,[],[f20558]) ).
fof(f47586,plain,
( spl22_1326
| ~ spl22_118
| ~ spl22_961 ),
inference(avatar_split_clause,[],[f22916,f20558,f1074,f47584]) ).
fof(f47584,plain,
( spl22_1326
<=> ! [X7] :
( ~ empty(relation_dom_restriction(sK5,X7))
| sK15 = relation_rng(set_intersection2(X7,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1326])]) ).
fof(f1074,plain,
( spl22_118
<=> ! [X0] :
( relation_rng(X0) = sK15
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_118])]) ).
fof(f22916,plain,
( ! [X7] :
( ~ empty(relation_dom_restriction(sK5,X7))
| sK15 = relation_rng(set_intersection2(X7,relation_dom(sK5))) )
| ~ spl22_118
| ~ spl22_961 ),
inference(resolution,[],[f20559,f1075]) ).
fof(f1075,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK15 )
| ~ spl22_118 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f46606,plain,
( spl22_1325
| ~ spl22_384
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15110,f15007,f4578,f46604]) ).
fof(f46604,plain,
( spl22_1325
<=> ! [X126] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK5),X126))
| ~ sP0(relation_dom_restriction(sK5,X126),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1325])]) ).
fof(f4578,plain,
( spl22_384
<=> ! [X14] :
( ~ sP0(sK5,relation_dom(X14))
| ~ sP0(X14,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_384])]) ).
fof(f15110,plain,
( ! [X126] :
( ~ sP0(sK5,set_intersection2(relation_dom(sK5),X126))
| ~ sP0(relation_dom_restriction(sK5,X126),sK15) )
| ~ spl22_384
| ~ spl22_823 ),
inference(superposition,[],[f4579,f15008]) ).
fof(f4579,plain,
( ! [X14] :
( ~ sP0(sK5,relation_dom(X14))
| ~ sP0(X14,sK15) )
| ~ spl22_384 ),
inference(avatar_component_clause,[],[f4578]) ).
fof(f43206,plain,
( spl22_1324
| ~ spl22_124
| ~ spl22_1271 ),
inference(avatar_split_clause,[],[f39932,f39711,f1103,f43204]) ).
fof(f43204,plain,
( spl22_1324
<=> ! [X66] :
( ~ sP0(relation_dom_restriction(sK5,X66),sK15)
| empty(set_intersection2(X66,relation_dom(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1324])]) ).
fof(f39932,plain,
( ! [X66] :
( ~ sP0(relation_dom_restriction(sK5,X66),sK15)
| empty(set_intersection2(X66,relation_dom(sK5))) )
| ~ spl22_124
| ~ spl22_1271 ),
inference(resolution,[],[f39712,f1104]) ).
fof(f40156,plain,
( spl22_1323
| ~ spl22_45
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5220,f5211,f448,f40154]) ).
fof(f40154,plain,
( spl22_1323
<=> ! [X16,X15] :
( sP0(X15,X16)
| apply(relation_dom_restriction(sK15,X16),sK7(X15,X16)) = apply(sK15,sK7(X15,X16))
| ~ in(relation_dom(X15),sK8(X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1323])]) ).
fof(f5211,plain,
( spl22_405
<=> ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK7(X15,X14)) = apply(sK15,sK7(X15,X14))
| sP0(X15,X14)
| in(sK8(X15,X14),relation_dom(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_405])]) ).
fof(f5220,plain,
( ! [X16,X15] :
( sP0(X15,X16)
| apply(relation_dom_restriction(sK15,X16),sK7(X15,X16)) = apply(sK15,sK7(X15,X16))
| ~ in(relation_dom(X15),sK8(X15,X16)) )
| ~ spl22_45
| ~ spl22_405 ),
inference(resolution,[],[f5212,f449]) ).
fof(f5212,plain,
( ! [X14,X15] :
( in(sK8(X15,X14),relation_dom(X15))
| sP0(X15,X14)
| apply(relation_dom_restriction(sK15,X14),sK7(X15,X14)) = apply(sK15,sK7(X15,X14)) )
| ~ spl22_405 ),
inference(avatar_component_clause,[],[f5211]) ).
fof(f40152,plain,
( ~ spl22_1322
| ~ spl22_840
| ~ spl22_1271 ),
inference(avatar_split_clause,[],[f39906,f39711,f15376,f40149]) ).
fof(f40149,plain,
( spl22_1322
<=> sP0(relation_dom_restriction(sK5,sK3),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1322])]) ).
fof(f15376,plain,
( spl22_840
<=> in(sK4,set_intersection2(sK3,relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_840])]) ).
fof(f39906,plain,
( ~ sP0(relation_dom_restriction(sK5,sK3),sK15)
| ~ spl22_840
| ~ spl22_1271 ),
inference(resolution,[],[f39712,f15377]) ).
fof(f15377,plain,
( in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_840 ),
inference(avatar_component_clause,[],[f15376]) ).
fof(f40147,plain,
( spl22_1321
| ~ spl22_46
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5219,f5211,f452,f40145]) ).
fof(f40145,plain,
( spl22_1321
<=> ! [X13,X14] :
( sP0(X13,X14)
| apply(relation_dom_restriction(sK15,X14),sK7(X13,X14)) = apply(sK15,sK7(X13,X14))
| element(sK8(X13,X14),relation_dom(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1321])]) ).
fof(f5219,plain,
( ! [X14,X13] :
( sP0(X13,X14)
| apply(relation_dom_restriction(sK15,X14),sK7(X13,X14)) = apply(sK15,sK7(X13,X14))
| element(sK8(X13,X14),relation_dom(X13)) )
| ~ spl22_46
| ~ spl22_405 ),
inference(resolution,[],[f5212,f453]) ).
fof(f40143,plain,
( spl22_1320
| ~ spl22_45
| ~ spl22_403 ),
inference(avatar_split_clause,[],[f5208,f5195,f448,f40141]) ).
fof(f40141,plain,
( spl22_1320
<=> ! [X16,X15] :
( sP0(X15,X16)
| apply(relation_dom_restriction(sK20,X16),sK7(X15,X16)) = apply(sK20,sK7(X15,X16))
| ~ in(relation_dom(X15),sK8(X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1320])]) ).
fof(f5195,plain,
( spl22_403
<=> ! [X29,X28] :
( apply(relation_dom_restriction(sK20,X28),sK7(X29,X28)) = apply(sK20,sK7(X29,X28))
| sP0(X29,X28)
| in(sK8(X29,X28),relation_dom(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_403])]) ).
fof(f5208,plain,
( ! [X16,X15] :
( sP0(X15,X16)
| apply(relation_dom_restriction(sK20,X16),sK7(X15,X16)) = apply(sK20,sK7(X15,X16))
| ~ in(relation_dom(X15),sK8(X15,X16)) )
| ~ spl22_45
| ~ spl22_403 ),
inference(resolution,[],[f5196,f449]) ).
fof(f5196,plain,
( ! [X28,X29] :
( in(sK8(X29,X28),relation_dom(X29))
| sP0(X29,X28)
| apply(relation_dom_restriction(sK20,X28),sK7(X29,X28)) = apply(sK20,sK7(X29,X28)) )
| ~ spl22_403 ),
inference(avatar_component_clause,[],[f5195]) ).
fof(f40139,plain,
( spl22_1319
| ~ spl22_46
| ~ spl22_403 ),
inference(avatar_split_clause,[],[f5207,f5195,f452,f40137]) ).
fof(f40137,plain,
( spl22_1319
<=> ! [X13,X14] :
( sP0(X13,X14)
| apply(relation_dom_restriction(sK20,X14),sK7(X13,X14)) = apply(sK20,sK7(X13,X14))
| element(sK8(X13,X14),relation_dom(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1319])]) ).
fof(f5207,plain,
( ! [X14,X13] :
( sP0(X13,X14)
| apply(relation_dom_restriction(sK20,X14),sK7(X13,X14)) = apply(sK20,sK7(X13,X14))
| element(sK8(X13,X14),relation_dom(X13)) )
| ~ spl22_46
| ~ spl22_403 ),
inference(resolution,[],[f5196,f453]) ).
fof(f40135,plain,
( spl22_1318
| ~ spl22_45
| ~ spl22_402 ),
inference(avatar_split_clause,[],[f5192,f5183,f448,f40133]) ).
fof(f40133,plain,
( spl22_1318
<=> ! [X16,X15] :
( sP0(X15,X16)
| apply(relation_dom_restriction(sK19,X16),sK7(X15,X16)) = apply(sK19,sK7(X15,X16))
| ~ in(relation_dom(X15),sK8(X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1318])]) ).
fof(f5183,plain,
( spl22_402
<=> ! [X27,X26] :
( apply(relation_dom_restriction(sK19,X26),sK7(X27,X26)) = apply(sK19,sK7(X27,X26))
| sP0(X27,X26)
| in(sK8(X27,X26),relation_dom(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_402])]) ).
fof(f5192,plain,
( ! [X16,X15] :
( sP0(X15,X16)
| apply(relation_dom_restriction(sK19,X16),sK7(X15,X16)) = apply(sK19,sK7(X15,X16))
| ~ in(relation_dom(X15),sK8(X15,X16)) )
| ~ spl22_45
| ~ spl22_402 ),
inference(resolution,[],[f5184,f449]) ).
fof(f5184,plain,
( ! [X26,X27] :
( in(sK8(X27,X26),relation_dom(X27))
| sP0(X27,X26)
| apply(relation_dom_restriction(sK19,X26),sK7(X27,X26)) = apply(sK19,sK7(X27,X26)) )
| ~ spl22_402 ),
inference(avatar_component_clause,[],[f5183]) ).
fof(f40131,plain,
( spl22_1317
| ~ spl22_46
| ~ spl22_402 ),
inference(avatar_split_clause,[],[f5191,f5183,f452,f40129]) ).
fof(f40129,plain,
( spl22_1317
<=> ! [X13,X14] :
( sP0(X13,X14)
| apply(relation_dom_restriction(sK19,X14),sK7(X13,X14)) = apply(sK19,sK7(X13,X14))
| element(sK8(X13,X14),relation_dom(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1317])]) ).
fof(f5191,plain,
( ! [X14,X13] :
( sP0(X13,X14)
| apply(relation_dom_restriction(sK19,X14),sK7(X13,X14)) = apply(sK19,sK7(X13,X14))
| element(sK8(X13,X14),relation_dom(X13)) )
| ~ spl22_46
| ~ spl22_402 ),
inference(resolution,[],[f5184,f453]) ).
fof(f40127,plain,
( spl22_1316
| ~ spl22_45
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5159,f5153,f448,f40125]) ).
fof(f40125,plain,
( spl22_1316
<=> ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK15,relation_dom(X7)),sK8(X7,X8)) = apply(sK15,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1316])]) ).
fof(f5159,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK15,relation_dom(X7)),sK8(X7,X8)) = apply(sK15,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) )
| ~ spl22_45
| ~ spl22_401 ),
inference(resolution,[],[f5154,f449]) ).
fof(f40123,plain,
( spl22_1315
| ~ spl22_46
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5158,f5153,f452,f40121]) ).
fof(f40121,plain,
( spl22_1315
<=> ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK15,relation_dom(X5)),sK8(X5,X6)) = apply(sK15,sK8(X5,X6))
| element(sK7(X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1315])]) ).
fof(f5158,plain,
( ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK15,relation_dom(X5)),sK8(X5,X6)) = apply(sK15,sK8(X5,X6))
| element(sK7(X5,X6),X6) )
| ~ spl22_46
| ~ spl22_401 ),
inference(resolution,[],[f5154,f453]) ).
fof(f40119,plain,
( spl22_1314
| ~ spl22_45
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5129,f5123,f448,f40117]) ).
fof(f40117,plain,
( spl22_1314
<=> ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK20,relation_dom(X7)),sK8(X7,X8)) = apply(sK20,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1314])]) ).
fof(f5129,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK20,relation_dom(X7)),sK8(X7,X8)) = apply(sK20,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) )
| ~ spl22_45
| ~ spl22_400 ),
inference(resolution,[],[f5124,f449]) ).
fof(f40115,plain,
( spl22_1313
| ~ spl22_46
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5128,f5123,f452,f40113]) ).
fof(f40113,plain,
( spl22_1313
<=> ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK20,relation_dom(X5)),sK8(X5,X6)) = apply(sK20,sK8(X5,X6))
| element(sK7(X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1313])]) ).
fof(f5128,plain,
( ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK20,relation_dom(X5)),sK8(X5,X6)) = apply(sK20,sK8(X5,X6))
| element(sK7(X5,X6),X6) )
| ~ spl22_46
| ~ spl22_400 ),
inference(resolution,[],[f5124,f453]) ).
fof(f40111,plain,
( spl22_1312
| ~ spl22_45
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5099,f5093,f448,f40109]) ).
fof(f40109,plain,
( spl22_1312
<=> ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK19,relation_dom(X7)),sK8(X7,X8)) = apply(sK19,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1312])]) ).
fof(f5099,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK19,relation_dom(X7)),sK8(X7,X8)) = apply(sK19,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) )
| ~ spl22_45
| ~ spl22_399 ),
inference(resolution,[],[f5094,f449]) ).
fof(f39900,plain,
( spl22_1311
| ~ spl22_46
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5098,f5093,f452,f39898]) ).
fof(f39898,plain,
( spl22_1311
<=> ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK19,relation_dom(X5)),sK8(X5,X6)) = apply(sK19,sK8(X5,X6))
| element(sK7(X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1311])]) ).
fof(f5098,plain,
( ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK19,relation_dom(X5)),sK8(X5,X6)) = apply(sK19,sK8(X5,X6))
| element(sK7(X5,X6),X6) )
| ~ spl22_46
| ~ spl22_399 ),
inference(resolution,[],[f5094,f453]) ).
fof(f39896,plain,
( spl22_1310
| ~ spl22_124
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5035,f4961,f1103,f39894]) ).
fof(f39894,plain,
( spl22_1310
<=> ! [X22,X21] :
( sK7(X21,powerset(X22)) = apply(X21,sK8(X21,powerset(X22)))
| ~ empty(X22)
| sP0(X21,powerset(X22))
| empty(sK7(X21,powerset(X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1310])]) ).
fof(f5035,plain,
( ! [X21,X22] :
( sK7(X21,powerset(X22)) = apply(X21,sK8(X21,powerset(X22)))
| ~ empty(X22)
| sP0(X21,powerset(X22))
| empty(sK7(X21,powerset(X22))) )
| ~ spl22_124
| ~ spl22_395 ),
inference(resolution,[],[f4962,f1104]) ).
fof(f39892,plain,
( spl22_1309
| ~ spl22_36
| ~ spl22_393 ),
inference(avatar_split_clause,[],[f5007,f4950,f393,f39890]) ).
fof(f39890,plain,
( spl22_1309
<=> ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1309])]) ).
fof(f393,plain,
( spl22_36
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_36])]) ).
fof(f4950,plain,
( spl22_393
<=> ! [X2,X4,X3] :
( sP0(X2,X3)
| ~ empty(relation_dom(X2))
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_393])]) ).
fof(f5007,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_393 ),
inference(resolution,[],[f4951,f394]) ).
fof(f394,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_36 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f4951,plain,
( ! [X2,X3,X4] :
( ~ empty(relation_dom(X2))
| sP0(X2,X3)
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_393 ),
inference(avatar_component_clause,[],[f4950]) ).
fof(f39888,plain,
( spl22_1308
| ~ spl22_45
| ~ spl22_379 ),
inference(avatar_split_clause,[],[f4693,f4558,f448,f39886]) ).
fof(f39886,plain,
( spl22_1308
<=> ! [X16,X14,X15] :
( element(sK13(sK10(powerset(X14)),X15,X16),X14)
| sP2(sK10(powerset(X14)),X15,X16)
| ~ in(X16,sK13(sK10(powerset(X14)),X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1308])]) ).
fof(f4693,plain,
( ! [X16,X14,X15] :
( element(sK13(sK10(powerset(X14)),X15,X16),X14)
| sP2(sK10(powerset(X14)),X15,X16)
| ~ in(X16,sK13(sK10(powerset(X14)),X15,X16)) )
| ~ spl22_45
| ~ spl22_379 ),
inference(resolution,[],[f4559,f449]) ).
fof(f39884,plain,
( spl22_1307
| ~ spl22_45
| ~ spl22_378 ),
inference(avatar_split_clause,[],[f4664,f4554,f448,f39882]) ).
fof(f39882,plain,
( spl22_1307
<=> ! [X16,X14,X15] :
( element(sK13(X14,sK10(powerset(X15)),X16),X15)
| sP2(X14,sK10(powerset(X15)),X16)
| ~ in(X16,sK13(X14,sK10(powerset(X15)),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1307])]) ).
fof(f4664,plain,
( ! [X16,X14,X15] :
( element(sK13(X14,sK10(powerset(X15)),X16),X15)
| sP2(X14,sK10(powerset(X15)),X16)
| ~ in(X16,sK13(X14,sK10(powerset(X15)),X16)) )
| ~ spl22_45
| ~ spl22_378 ),
inference(resolution,[],[f4555,f449]) ).
fof(f39880,plain,
( spl22_1306
| ~ spl22_45
| ~ spl22_377 ),
inference(avatar_split_clause,[],[f4635,f4550,f448,f39878]) ).
fof(f39878,plain,
( spl22_1306
<=> ! [X16,X14,X15] :
( element(sK13(X14,X15,sK10(powerset(X16))),X16)
| sP2(X14,X15,sK10(powerset(X16)))
| ~ in(X15,sK13(X14,X15,sK10(powerset(X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1306])]) ).
fof(f4635,plain,
( ! [X16,X14,X15] :
( element(sK13(X14,X15,sK10(powerset(X16))),X16)
| sP2(X14,X15,sK10(powerset(X16)))
| ~ in(X15,sK13(X14,X15,sK10(powerset(X16)))) )
| ~ spl22_45
| ~ spl22_377 ),
inference(resolution,[],[f4551,f449]) ).
fof(f39876,plain,
( spl22_1305
| ~ spl22_45
| ~ spl22_376 ),
inference(avatar_split_clause,[],[f4606,f4546,f448,f39874]) ).
fof(f39874,plain,
( spl22_1305
<=> ! [X13,X14,X15] :
( element(sK13(X13,X14,sK10(powerset(X15))),X15)
| sP2(X13,X14,sK10(powerset(X15)))
| ~ in(X13,sK13(X13,X14,sK10(powerset(X15)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1305])]) ).
fof(f4606,plain,
( ! [X14,X15,X13] :
( element(sK13(X13,X14,sK10(powerset(X15))),X15)
| sP2(X13,X14,sK10(powerset(X15)))
| ~ in(X13,sK13(X13,X14,sK10(powerset(X15)))) )
| ~ spl22_45
| ~ spl22_376 ),
inference(resolution,[],[f4547,f449]) ).
fof(f39872,plain,
( spl22_1304
| ~ spl22_255
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4491,f4164,f2711,f39870]) ).
fof(f39870,plain,
( spl22_1304
<=> ! [X189,X188,X190,X191] :
( sP2(powerset(X188),X189,X190)
| ~ empty(X188)
| in(sK13(powerset(X188),X189,X190),X190)
| sP2(sK15,X191,sK13(powerset(X188),X189,X190)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1304])]) ).
fof(f4491,plain,
( ! [X191,X188,X189,X190] :
( sP2(powerset(X188),X189,X190)
| ~ empty(X188)
| in(sK13(powerset(X188),X189,X190),X190)
| sP2(sK15,X191,sK13(powerset(X188),X189,X190)) )
| ~ spl22_255
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2712]) ).
fof(f39868,plain,
( spl22_1303
| ~ spl22_254
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4487,f4164,f2707,f39866]) ).
fof(f39866,plain,
( spl22_1303
<=> ! [X172,X169,X171,X170] :
( sP2(powerset(X169),X170,X171)
| ~ empty(X169)
| in(sK13(powerset(X169),X170,X171),X171)
| sP2(X172,sK15,sK13(powerset(X169),X170,X171)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1303])]) ).
fof(f4487,plain,
( ! [X170,X171,X169,X172] :
( sP2(powerset(X169),X170,X171)
| ~ empty(X169)
| in(sK13(powerset(X169),X170,X171),X171)
| sP2(X172,sK15,sK13(powerset(X169),X170,X171)) )
| ~ spl22_254
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2708]) ).
fof(f39864,plain,
( spl22_1302
| ~ spl22_253
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4483,f4164,f2703,f39862]) ).
fof(f39862,plain,
( spl22_1302
<=> ! [X150,X151,X152,X153] :
( sP2(powerset(X150),X151,X152)
| ~ empty(X150)
| in(sK13(powerset(X150),X151,X152),X152)
| sP2(X153,sK13(powerset(X150),X151,X152),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1302])]) ).
fof(f4483,plain,
( ! [X152,X150,X153,X151] :
( sP2(powerset(X150),X151,X152)
| ~ empty(X150)
| in(sK13(powerset(X150),X151,X152),X152)
| sP2(X153,sK13(powerset(X150),X151,X152),sK15) )
| ~ spl22_253
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2704]) ).
fof(f39850,plain,
( spl22_1301
| ~ spl22_252
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4482,f4164,f2699,f39848]) ).
fof(f39848,plain,
( spl22_1301
<=> ! [X149,X146,X147,X148] :
( sP2(powerset(X146),X147,X148)
| ~ empty(X146)
| in(sK13(powerset(X146),X147,X148),X148)
| sP2(sK13(powerset(X146),X147,X148),X149,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1301])]) ).
fof(f4482,plain,
( ! [X148,X149,X146,X147] :
( sP2(powerset(X146),X147,X148)
| ~ empty(X146)
| in(sK13(powerset(X146),X147,X148),X148)
| sP2(sK13(powerset(X146),X147,X148),X149,sK15) )
| ~ spl22_252
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2700]) ).
fof(f39846,plain,
( spl22_1300
| ~ spl22_255
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4440,f4156,f2711,f39844]) ).
fof(f39844,plain,
( spl22_1300
<=> ! [X189,X188,X190,X191] :
( sP2(X188,X189,powerset(X190))
| ~ empty(X190)
| in(sK13(X188,X189,powerset(X190)),X188)
| sP2(sK15,X191,sK13(X188,X189,powerset(X190))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1300])]) ).
fof(f4440,plain,
( ! [X191,X188,X189,X190] :
( sP2(X188,X189,powerset(X190))
| ~ empty(X190)
| in(sK13(X188,X189,powerset(X190)),X188)
| sP2(sK15,X191,sK13(X188,X189,powerset(X190))) )
| ~ spl22_255
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2712]) ).
fof(f39842,plain,
( spl22_1299
| ~ spl22_254
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4436,f4156,f2707,f39840]) ).
fof(f39840,plain,
( spl22_1299
<=> ! [X172,X169,X171,X170] :
( sP2(X169,X170,powerset(X171))
| ~ empty(X171)
| in(sK13(X169,X170,powerset(X171)),X169)
| sP2(X172,sK15,sK13(X169,X170,powerset(X171))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1299])]) ).
fof(f4436,plain,
( ! [X170,X171,X169,X172] :
( sP2(X169,X170,powerset(X171))
| ~ empty(X171)
| in(sK13(X169,X170,powerset(X171)),X169)
| sP2(X172,sK15,sK13(X169,X170,powerset(X171))) )
| ~ spl22_254
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2708]) ).
fof(f39838,plain,
( spl22_1298
| ~ spl22_253
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4432,f4156,f2703,f39836]) ).
fof(f39836,plain,
( spl22_1298
<=> ! [X150,X151,X152,X153] :
( sP2(X150,X151,powerset(X152))
| ~ empty(X152)
| in(sK13(X150,X151,powerset(X152)),X150)
| sP2(X153,sK13(X150,X151,powerset(X152)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1298])]) ).
fof(f4432,plain,
( ! [X152,X150,X153,X151] :
( sP2(X150,X151,powerset(X152))
| ~ empty(X152)
| in(sK13(X150,X151,powerset(X152)),X150)
| sP2(X153,sK13(X150,X151,powerset(X152)),sK15) )
| ~ spl22_253
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2704]) ).
fof(f39834,plain,
( spl22_1297
| ~ spl22_252
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4431,f4156,f2699,f39832]) ).
fof(f39832,plain,
( spl22_1297
<=> ! [X149,X146,X147,X148] :
( sP2(X146,X147,powerset(X148))
| ~ empty(X148)
| in(sK13(X146,X147,powerset(X148)),X146)
| sP2(sK13(X146,X147,powerset(X148)),X149,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1297])]) ).
fof(f4431,plain,
( ! [X148,X149,X146,X147] :
( sP2(X146,X147,powerset(X148))
| ~ empty(X148)
| in(sK13(X146,X147,powerset(X148)),X146)
| sP2(sK13(X146,X147,powerset(X148)),X149,sK15) )
| ~ spl22_252
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2700]) ).
fof(f39830,plain,
( spl22_1296
| ~ spl22_255
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4389,f4148,f2711,f39828]) ).
fof(f39828,plain,
( spl22_1296
<=> ! [X189,X188,X190,X191] :
( sP2(X188,powerset(X189),X190)
| ~ empty(X189)
| in(sK13(X188,powerset(X189),X190),X190)
| sP2(sK15,X191,sK13(X188,powerset(X189),X190)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1296])]) ).
fof(f4389,plain,
( ! [X191,X188,X189,X190] :
( sP2(X188,powerset(X189),X190)
| ~ empty(X189)
| in(sK13(X188,powerset(X189),X190),X190)
| sP2(sK15,X191,sK13(X188,powerset(X189),X190)) )
| ~ spl22_255
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2712]) ).
fof(f39826,plain,
( spl22_1295
| ~ spl22_254
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4385,f4148,f2707,f39824]) ).
fof(f39824,plain,
( spl22_1295
<=> ! [X172,X169,X171,X170] :
( sP2(X169,powerset(X170),X171)
| ~ empty(X170)
| in(sK13(X169,powerset(X170),X171),X171)
| sP2(X172,sK15,sK13(X169,powerset(X170),X171)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1295])]) ).
fof(f4385,plain,
( ! [X170,X171,X169,X172] :
( sP2(X169,powerset(X170),X171)
| ~ empty(X170)
| in(sK13(X169,powerset(X170),X171),X171)
| sP2(X172,sK15,sK13(X169,powerset(X170),X171)) )
| ~ spl22_254
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2708]) ).
fof(f39822,plain,
( spl22_1294
| ~ spl22_253
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4381,f4148,f2703,f39820]) ).
fof(f39820,plain,
( spl22_1294
<=> ! [X150,X151,X152,X153] :
( sP2(X150,powerset(X151),X152)
| ~ empty(X151)
| in(sK13(X150,powerset(X151),X152),X152)
| sP2(X153,sK13(X150,powerset(X151),X152),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1294])]) ).
fof(f4381,plain,
( ! [X152,X150,X153,X151] :
( sP2(X150,powerset(X151),X152)
| ~ empty(X151)
| in(sK13(X150,powerset(X151),X152),X152)
| sP2(X153,sK13(X150,powerset(X151),X152),sK15) )
| ~ spl22_253
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2704]) ).
fof(f39818,plain,
( spl22_1293
| ~ spl22_252
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4380,f4148,f2699,f39816]) ).
fof(f39816,plain,
( spl22_1293
<=> ! [X149,X146,X147,X148] :
( sP2(X146,powerset(X147),X148)
| ~ empty(X147)
| in(sK13(X146,powerset(X147),X148),X148)
| sP2(sK13(X146,powerset(X147),X148),X149,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1293])]) ).
fof(f4380,plain,
( ! [X148,X149,X146,X147] :
( sP2(X146,powerset(X147),X148)
| ~ empty(X147)
| in(sK13(X146,powerset(X147),X148),X148)
| sP2(sK13(X146,powerset(X147),X148),X149,sK15) )
| ~ spl22_252
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2700]) ).
fof(f39814,plain,
( spl22_1292
| ~ spl22_255
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4338,f4139,f2711,f39812]) ).
fof(f39812,plain,
( spl22_1292
<=> ! [X189,X188,X190,X191] :
( sP2(X188,X189,powerset(X190))
| ~ empty(X190)
| in(sK13(X188,X189,powerset(X190)),X189)
| sP2(sK15,X191,sK13(X188,X189,powerset(X190))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1292])]) ).
fof(f4338,plain,
( ! [X191,X188,X189,X190] :
( sP2(X188,X189,powerset(X190))
| ~ empty(X190)
| in(sK13(X188,X189,powerset(X190)),X189)
| sP2(sK15,X191,sK13(X188,X189,powerset(X190))) )
| ~ spl22_255
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2712]) ).
fof(f39800,plain,
( spl22_1291
| ~ spl22_254
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4334,f4139,f2707,f39798]) ).
fof(f39798,plain,
( spl22_1291
<=> ! [X172,X169,X171,X170] :
( sP2(X169,X170,powerset(X171))
| ~ empty(X171)
| in(sK13(X169,X170,powerset(X171)),X170)
| sP2(X172,sK15,sK13(X169,X170,powerset(X171))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1291])]) ).
fof(f4334,plain,
( ! [X170,X171,X169,X172] :
( sP2(X169,X170,powerset(X171))
| ~ empty(X171)
| in(sK13(X169,X170,powerset(X171)),X170)
| sP2(X172,sK15,sK13(X169,X170,powerset(X171))) )
| ~ spl22_254
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2708]) ).
fof(f39796,plain,
( spl22_1290
| ~ spl22_253
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4330,f4139,f2703,f39794]) ).
fof(f39794,plain,
( spl22_1290
<=> ! [X150,X151,X152,X153] :
( sP2(X150,X151,powerset(X152))
| ~ empty(X152)
| in(sK13(X150,X151,powerset(X152)),X151)
| sP2(X153,sK13(X150,X151,powerset(X152)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1290])]) ).
fof(f4330,plain,
( ! [X152,X150,X153,X151] :
( sP2(X150,X151,powerset(X152))
| ~ empty(X152)
| in(sK13(X150,X151,powerset(X152)),X151)
| sP2(X153,sK13(X150,X151,powerset(X152)),sK15) )
| ~ spl22_253
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2704]) ).
fof(f39792,plain,
( spl22_1289
| ~ spl22_252
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4329,f4139,f2699,f39790]) ).
fof(f39790,plain,
( spl22_1289
<=> ! [X149,X146,X147,X148] :
( sP2(X146,X147,powerset(X148))
| ~ empty(X148)
| in(sK13(X146,X147,powerset(X148)),X147)
| sP2(sK13(X146,X147,powerset(X148)),X149,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1289])]) ).
fof(f4329,plain,
( ! [X148,X149,X146,X147] :
( sP2(X146,X147,powerset(X148))
| ~ empty(X148)
| in(sK13(X146,X147,powerset(X148)),X147)
| sP2(sK13(X146,X147,powerset(X148)),X149,sK15) )
| ~ spl22_252
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2700]) ).
fof(f39788,plain,
( spl22_1288
| ~ spl22_56
| ~ spl22_359 ),
inference(avatar_split_clause,[],[f4079,f4035,f540,f39786]) ).
fof(f39786,plain,
( spl22_1288
<=> ! [X9,X8] :
( element(sK8(X8,sK10(powerset(X9))),relation_dom(X8))
| sP0(X8,sK10(powerset(X9)))
| empty(X9)
| in(sK7(X8,sK10(powerset(X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1288])]) ).
fof(f4079,plain,
( ! [X8,X9] :
( element(sK8(X8,sK10(powerset(X9))),relation_dom(X8))
| sP0(X8,sK10(powerset(X9)))
| empty(X9)
| in(sK7(X8,sK10(powerset(X9))),X9) )
| ~ spl22_56
| ~ spl22_359 ),
inference(resolution,[],[f4036,f541]) ).
fof(f39784,plain,
( spl22_1287
| ~ spl22_56
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4064,f4027,f540,f39782]) ).
fof(f39782,plain,
( spl22_1287
<=> ! [X9,X8] :
( in(sK8(X8,sK10(powerset(X9))),relation_dom(X8))
| sP0(X8,sK10(powerset(X9)))
| empty(X9)
| in(sK7(X8,sK10(powerset(X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1287])]) ).
fof(f4064,plain,
( ! [X8,X9] :
( in(sK8(X8,sK10(powerset(X9))),relation_dom(X8))
| sP0(X8,sK10(powerset(X9)))
| empty(X9)
| in(sK7(X8,sK10(powerset(X9))),X9) )
| ~ spl22_56
| ~ spl22_357 ),
inference(resolution,[],[f4028,f541]) ).
fof(f39780,plain,
( spl22_1286
| ~ spl22_156
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3919,f3857,f1407,f39778]) ).
fof(f39778,plain,
( spl22_1286
<=> ! [X85,X83,X84,X86] :
( sP0(X83,powerset(X84))
| ~ empty(X84)
| in(sK8(X83,powerset(X84)),relation_dom(X83))
| sP2(sK7(X83,powerset(X84)),X85,X86)
| ~ empty(X86) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1286])]) ).
fof(f3919,plain,
( ! [X83,X86,X84,X85] :
( sP0(X83,powerset(X84))
| ~ empty(X84)
| in(sK8(X83,powerset(X84)),relation_dom(X83))
| sP2(sK7(X83,powerset(X84)),X85,X86)
| ~ empty(X86) )
| ~ spl22_156
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1408]) ).
fof(f39776,plain,
( spl22_1285
| ~ spl22_154
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3915,f3857,f1399,f39774]) ).
fof(f39774,plain,
( spl22_1285
<=> ! [X69,X70,X67,X68] :
( sP0(X67,powerset(X68))
| ~ empty(X68)
| in(sK8(X67,powerset(X68)),relation_dom(X67))
| sP2(X69,sK7(X67,powerset(X68)),X70)
| ~ empty(X70) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1285])]) ).
fof(f3915,plain,
( ! [X70,X68,X69,X67] :
( sP0(X67,powerset(X68))
| ~ empty(X68)
| in(sK8(X67,powerset(X68)),relation_dom(X67))
| sP2(X69,sK7(X67,powerset(X68)),X70)
| ~ empty(X70) )
| ~ spl22_154
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1400]) ).
fof(f39772,plain,
( spl22_1284
| ~ spl22_157
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3908,f3857,f1411,f39770]) ).
fof(f39770,plain,
( spl22_1284
<=> ! [X41,X40,X42,X39] :
( sP0(X39,powerset(X40))
| ~ empty(X40)
| in(sK8(X39,powerset(X40)),relation_dom(X39))
| sP2(X41,X42,sK7(X39,powerset(X40)))
| ~ empty(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1284])]) ).
fof(f3908,plain,
( ! [X40,X41,X39,X42] :
( sP0(X39,powerset(X40))
| ~ empty(X40)
| in(sK8(X39,powerset(X40)),relation_dom(X39))
| sP2(X41,X42,sK7(X39,powerset(X40)))
| ~ empty(X41) )
| ~ spl22_157
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1412]) ).
fof(f39768,plain,
( spl22_1283
| ~ spl22_155
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3907,f3857,f1403,f39766]) ).
fof(f39766,plain,
( spl22_1283
<=> ! [X38,X36,X35,X37] :
( sP0(X35,powerset(X36))
| ~ empty(X36)
| in(sK8(X35,powerset(X36)),relation_dom(X35))
| sP2(X37,X38,sK7(X35,powerset(X36)))
| ~ empty(X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1283])]) ).
fof(f3907,plain,
( ! [X38,X36,X37,X35] :
( sP0(X35,powerset(X36))
| ~ empty(X36)
| in(sK8(X35,powerset(X36)),relation_dom(X35))
| sP2(X37,X38,sK7(X35,powerset(X36)))
| ~ empty(X38) )
| ~ spl22_155
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1404]) ).
fof(f39764,plain,
( spl22_1282
| ~ spl22_149
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3899,f3857,f1362,f39762]) ).
fof(f39762,plain,
( spl22_1282
<=> ! [X12,X11,X10] :
( sP0(X10,powerset(X11))
| ~ empty(X11)
| in(sK8(X10,powerset(X11)),relation_dom(X10))
| sP0(X12,sK7(X10,powerset(X11)))
| ~ empty(relation_dom(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1282])]) ).
fof(f3899,plain,
( ! [X10,X11,X12] :
( sP0(X10,powerset(X11))
| ~ empty(X11)
| in(sK8(X10,powerset(X11)),relation_dom(X10))
| sP0(X12,sK7(X10,powerset(X11)))
| ~ empty(relation_dom(X12)) )
| ~ spl22_149
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1363]) ).
fof(f39753,plain,
( spl22_1281
| ~ spl22_52
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f3840,f3831,f498,f39751]) ).
fof(f39751,plain,
( spl22_1281
<=> ! [X6,X7] :
( sP2(sK10(powerset(powerset(X6))),X7,sK10(powerset(powerset(X6))))
| subset(sK13(sK10(powerset(powerset(X6))),X7,sK10(powerset(powerset(X6)))),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1281])]) ).
fof(f3840,plain,
( ! [X6,X7] :
( sP2(sK10(powerset(powerset(X6))),X7,sK10(powerset(powerset(X6))))
| subset(sK13(sK10(powerset(powerset(X6))),X7,sK10(powerset(powerset(X6)))),X6) )
| ~ spl22_52
| ~ spl22_347 ),
inference(resolution,[],[f3832,f499]) ).
fof(f39749,plain,
( spl22_1280
| ~ spl22_52
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f3836,f3827,f498,f39747]) ).
fof(f39747,plain,
( spl22_1280
<=> ! [X6,X7] :
( sP2(X6,sK10(powerset(powerset(X7))),sK10(powerset(powerset(X7))))
| subset(sK13(X6,sK10(powerset(powerset(X7))),sK10(powerset(powerset(X7)))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1280])]) ).
fof(f3836,plain,
( ! [X6,X7] :
( sP2(X6,sK10(powerset(powerset(X7))),sK10(powerset(powerset(X7))))
| subset(sK13(X6,sK10(powerset(powerset(X7))),sK10(powerset(powerset(X7)))),X7) )
| ~ spl22_52
| ~ spl22_346 ),
inference(resolution,[],[f3828,f499]) ).
fof(f39745,plain,
( spl22_1279
| ~ spl22_67
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f3725,f3433,f633,f39743]) ).
fof(f39743,plain,
( spl22_1279
<=> ! [X5,X4,X7,X6] :
( element(sK13(powerset(X4),X5,X6),X6)
| sP2(powerset(X4),X5,X6)
| element(X7,X4)
| ~ in(X7,sK13(powerset(X4),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1279])]) ).
fof(f3433,plain,
( spl22_333
<=> ! [X9,X11,X10] :
( element(sK13(X9,X10,X11),X11)
| sP2(X9,X10,X11)
| element(sK13(X9,X10,X11),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_333])]) ).
fof(f3725,plain,
( ! [X6,X7,X4,X5] :
( element(sK13(powerset(X4),X5,X6),X6)
| sP2(powerset(X4),X5,X6)
| element(X7,X4)
| ~ in(X7,sK13(powerset(X4),X5,X6)) )
| ~ spl22_67
| ~ spl22_333 ),
inference(resolution,[],[f3434,f634]) ).
fof(f3434,plain,
( ! [X10,X11,X9] :
( element(sK13(X9,X10,X11),X11)
| element(sK13(X9,X10,X11),X9)
| sP2(X9,X10,X11) )
| ~ spl22_333 ),
inference(avatar_component_clause,[],[f3433]) ).
fof(f39741,plain,
( spl22_1278
| ~ spl22_67
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f3721,f3433,f633,f39739]) ).
fof(f39739,plain,
( spl22_1278
<=> ! [X5,X4,X7,X6] :
( element(sK13(X4,X5,powerset(X6)),X4)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1278])]) ).
fof(f3721,plain,
( ! [X6,X7,X4,X5] :
( element(sK13(X4,X5,powerset(X6)),X4)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) )
| ~ spl22_67
| ~ spl22_333 ),
inference(resolution,[],[f3434,f634]) ).
fof(f39737,plain,
( spl22_1277
| ~ spl22_67
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3702,f3396,f633,f39735]) ).
fof(f39735,plain,
( spl22_1277
<=> ! [X5,X4,X7,X6] :
( element(sK13(X4,powerset(X5),X6),X6)
| sP2(X4,powerset(X5),X6)
| element(X7,X5)
| ~ in(X7,sK13(X4,powerset(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1277])]) ).
fof(f3396,plain,
( spl22_328
<=> ! [X9,X11,X10] :
( element(sK13(X9,X10,X11),X11)
| sP2(X9,X10,X11)
| element(sK13(X9,X10,X11),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_328])]) ).
fof(f3702,plain,
( ! [X6,X7,X4,X5] :
( element(sK13(X4,powerset(X5),X6),X6)
| sP2(X4,powerset(X5),X6)
| element(X7,X5)
| ~ in(X7,sK13(X4,powerset(X5),X6)) )
| ~ spl22_67
| ~ spl22_328 ),
inference(resolution,[],[f3397,f634]) ).
fof(f3397,plain,
( ! [X10,X11,X9] :
( element(sK13(X9,X10,X11),X11)
| element(sK13(X9,X10,X11),X10)
| sP2(X9,X10,X11) )
| ~ spl22_328 ),
inference(avatar_component_clause,[],[f3396]) ).
fof(f39733,plain,
( spl22_1276
| ~ spl22_67
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3698,f3396,f633,f39731]) ).
fof(f39731,plain,
( spl22_1276
<=> ! [X5,X4,X7,X6] :
( element(sK13(X4,X5,powerset(X6)),X5)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1276])]) ).
fof(f3698,plain,
( ! [X6,X7,X4,X5] :
( element(sK13(X4,X5,powerset(X6)),X5)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) )
| ~ spl22_67
| ~ spl22_328 ),
inference(resolution,[],[f3397,f634]) ).
fof(f39729,plain,
( spl22_1275
| ~ spl22_67
| ~ spl22_326 ),
inference(avatar_split_clause,[],[f3689,f3388,f633,f39727]) ).
fof(f39727,plain,
( spl22_1275
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X4,X5,sK6(powerset(X6)))
| empty(powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,sK6(powerset(X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1275])]) ).
fof(f3388,plain,
( spl22_326
<=> ! [X18,X16,X17] :
( sP2(X16,X17,sK6(X18))
| ~ empty(X16)
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_326])]) ).
fof(f3689,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X4,X5,sK6(powerset(X6)))
| empty(powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,sK6(powerset(X6)))) )
| ~ spl22_67
| ~ spl22_326 ),
inference(resolution,[],[f3389,f634]) ).
fof(f3389,plain,
( ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X18)
| ~ empty(X16)
| sP2(X16,X17,sK6(X18))
| empty(X18) )
| ~ spl22_326 ),
inference(avatar_component_clause,[],[f3388]) ).
fof(f39725,plain,
( spl22_1274
| ~ spl22_67
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3680,f3380,f633,f39723]) ).
fof(f39723,plain,
( spl22_1274
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(sK6(powerset(X5)),X6,X4)
| empty(powerset(X5))
| element(X7,X5)
| ~ in(X7,sK13(sK6(powerset(X5)),X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1274])]) ).
fof(f3380,plain,
( spl22_324
<=> ! [X16,X17,X15] :
( sP2(sK6(X15),X16,X17)
| ~ empty(X17)
| element(sK13(sK6(X15),X16,X17),X15)
| empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_324])]) ).
fof(f3680,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(sK6(powerset(X5)),X6,X4)
| empty(powerset(X5))
| element(X7,X5)
| ~ in(X7,sK13(sK6(powerset(X5)),X6,X4)) )
| ~ spl22_67
| ~ spl22_324 ),
inference(resolution,[],[f3381,f634]) ).
fof(f3381,plain,
( ! [X16,X17,X15] :
( element(sK13(sK6(X15),X16,X17),X15)
| ~ empty(X17)
| sP2(sK6(X15),X16,X17)
| empty(X15) )
| ~ spl22_324 ),
inference(avatar_component_clause,[],[f3380]) ).
fof(f39721,plain,
( spl22_1273
| ~ spl22_67
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3663,f3372,f633,f39719]) ).
fof(f39719,plain,
( spl22_1273
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X5,X4,sK6(powerset(X6)))
| empty(powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X5,X4,sK6(powerset(X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1273])]) ).
fof(f3372,plain,
( spl22_322
<=> ! [X18,X16,X17] :
( sP2(X16,X17,sK6(X18))
| ~ empty(X17)
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_322])]) ).
fof(f3663,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X5,X4,sK6(powerset(X6)))
| empty(powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X5,X4,sK6(powerset(X6)))) )
| ~ spl22_67
| ~ spl22_322 ),
inference(resolution,[],[f3373,f634]) ).
fof(f3373,plain,
( ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X18)
| ~ empty(X17)
| sP2(X16,X17,sK6(X18))
| empty(X18) )
| ~ spl22_322 ),
inference(avatar_component_clause,[],[f3372]) ).
fof(f39717,plain,
( spl22_1272
| ~ spl22_67
| ~ spl22_320 ),
inference(avatar_split_clause,[],[f3654,f3364,f633,f39715]) ).
fof(f39715,plain,
( spl22_1272
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X5,sK6(powerset(X6)),X4)
| empty(powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X5,sK6(powerset(X6)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1272])]) ).
fof(f3364,plain,
( spl22_320
<=> ! [X16,X17,X15] :
( sP2(X15,sK6(X16),X17)
| ~ empty(X17)
| element(sK13(X15,sK6(X16),X17),X16)
| empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_320])]) ).
fof(f3654,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X5,sK6(powerset(X6)),X4)
| empty(powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X5,sK6(powerset(X6)),X4)) )
| ~ spl22_67
| ~ spl22_320 ),
inference(resolution,[],[f3365,f634]) ).
fof(f3365,plain,
( ! [X16,X17,X15] :
( element(sK13(X15,sK6(X16),X17),X16)
| ~ empty(X17)
| sP2(X15,sK6(X16),X17)
| empty(X16) )
| ~ spl22_320 ),
inference(avatar_component_clause,[],[f3364]) ).
fof(f39713,plain,
( spl22_1271
| ~ spl22_51
| ~ spl22_1240 ),
inference(avatar_split_clause,[],[f37106,f35033,f494,f39711]) ).
fof(f35033,plain,
( spl22_1240
<=> ! [X93,X92] :
( ~ in(X93,set_intersection2(relation_dom(sK5),X92))
| ~ sP0(relation_dom_restriction(sK5,X92),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1240])]) ).
fof(f37106,plain,
( ! [X2,X1] :
( ~ in(X2,set_intersection2(X1,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,X1),sK15) )
| ~ spl22_51
| ~ spl22_1240 ),
inference(superposition,[],[f35034,f495]) ).
fof(f35034,plain,
( ! [X92,X93] :
( ~ in(X93,set_intersection2(relation_dom(sK5),X92))
| ~ sP0(relation_dom_restriction(sK5,X92),sK15) )
| ~ spl22_1240 ),
inference(avatar_component_clause,[],[f35033]) ).
fof(f39709,plain,
( spl22_1270
| ~ spl22_143
| ~ spl22_319 ),
inference(avatar_split_clause,[],[f3628,f3343,f1304,f39707]) ).
fof(f39707,plain,
( spl22_1270
<=> ! [X29,X28] :
( ~ in(sK13(X28,powerset(X29),X28),X28)
| sP2(X28,powerset(X29),X28)
| empty(powerset(X29))
| ~ subset(sK13(X28,powerset(X29),X28),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1270])]) ).
fof(f1304,plain,
( spl22_143
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_143])]) ).
fof(f3628,plain,
( ! [X28,X29] :
( ~ in(sK13(X28,powerset(X29),X28),X28)
| sP2(X28,powerset(X29),X28)
| empty(powerset(X29))
| ~ subset(sK13(X28,powerset(X29),X28),X29) )
| ~ spl22_143
| ~ spl22_319 ),
inference(resolution,[],[f3344,f1305]) ).
fof(f1305,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl22_143 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f39705,plain,
( spl22_1269
| ~ spl22_255
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3220,f3185,f2711,f39703]) ).
fof(f39703,plain,
( spl22_1269
<=> ! [X73,X72] :
( ~ sP1(X72)
| sK13(sK15,X73,relation_rng(X72)) = apply(X72,sK9(X72,sK13(sK15,X73,relation_rng(X72))))
| sP2(sK15,X73,relation_rng(X72)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1269])]) ).
fof(f3220,plain,
( ! [X72,X73] :
( ~ sP1(X72)
| sK13(sK15,X73,relation_rng(X72)) = apply(X72,sK9(X72,sK13(sK15,X73,relation_rng(X72))))
| sP2(sK15,X73,relation_rng(X72)) )
| ~ spl22_255
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2712]) ).
fof(f39701,plain,
( spl22_1268
| ~ spl22_254
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3219,f3185,f2707,f39699]) ).
fof(f39699,plain,
( spl22_1268
<=> ! [X70,X71] :
( ~ sP1(X70)
| sK13(X71,sK15,relation_rng(X70)) = apply(X70,sK9(X70,sK13(X71,sK15,relation_rng(X70))))
| sP2(X71,sK15,relation_rng(X70)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1268])]) ).
fof(f3219,plain,
( ! [X70,X71] :
( ~ sP1(X70)
| sK13(X71,sK15,relation_rng(X70)) = apply(X70,sK9(X70,sK13(X71,sK15,relation_rng(X70))))
| sP2(X71,sK15,relation_rng(X70)) )
| ~ spl22_254
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2708]) ).
fof(f39697,plain,
( spl22_1267
| ~ spl22_253
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3218,f3185,f2703,f39695]) ).
fof(f39695,plain,
( spl22_1267
<=> ! [X69,X68] :
( ~ sP1(X68)
| sK13(X69,relation_rng(X68),sK15) = apply(X68,sK9(X68,sK13(X69,relation_rng(X68),sK15)))
| sP2(X69,relation_rng(X68),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1267])]) ).
fof(f3218,plain,
( ! [X68,X69] :
( ~ sP1(X68)
| sK13(X69,relation_rng(X68),sK15) = apply(X68,sK9(X68,sK13(X69,relation_rng(X68),sK15)))
| sP2(X69,relation_rng(X68),sK15) )
| ~ spl22_253
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2704]) ).
fof(f39693,plain,
( spl22_1266
| ~ spl22_252
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3217,f3185,f2699,f39691]) ).
fof(f39691,plain,
( spl22_1266
<=> ! [X66,X67] :
( ~ sP1(X66)
| sK13(relation_rng(X66),X67,sK15) = apply(X66,sK9(X66,sK13(relation_rng(X66),X67,sK15)))
| sP2(relation_rng(X66),X67,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1266])]) ).
fof(f3217,plain,
( ! [X66,X67] :
( ~ sP1(X66)
| sK13(relation_rng(X66),X67,sK15) = apply(X66,sK9(X66,sK13(relation_rng(X66),X67,sK15)))
| sP2(relation_rng(X66),X67,sK15) )
| ~ spl22_252
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2700]) ).
fof(f39689,plain,
( spl22_1265
| ~ spl22_149
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3195,f3185,f1362,f39687]) ).
fof(f39687,plain,
( spl22_1265
<=> ! [X7,X8] :
( ~ sP1(X7)
| sK7(X8,relation_rng(X7)) = apply(X7,sK9(X7,sK7(X8,relation_rng(X7))))
| sP0(X8,relation_rng(X7))
| ~ empty(relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1265])]) ).
fof(f3195,plain,
( ! [X8,X7] :
( ~ sP1(X7)
| sK7(X8,relation_rng(X7)) = apply(X7,sK9(X7,sK7(X8,relation_rng(X7))))
| sP0(X8,relation_rng(X7))
| ~ empty(relation_dom(X8)) )
| ~ spl22_149
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1363]) ).
fof(f39685,plain,
( spl22_1264
| ~ spl22_153
| ~ spl22_265 ),
inference(avatar_split_clause,[],[f2891,f2751,f1395,f39683]) ).
fof(f39683,plain,
( spl22_1264
<=> ! [X2,X0,X1] :
( sP2(apply(X0,X1),X2,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK13(apply(X0,X1),X2,apply(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1264])]) ).
fof(f2751,plain,
( spl22_265
<=> ! [X9,X10] :
( sP2(X9,X10,X9)
| ~ in(X9,sK13(X9,X10,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_265])]) ).
fof(f2891,plain,
( ! [X2,X0,X1] :
( sP2(apply(X0,X1),X2,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK13(apply(X0,X1),X2,apply(X0,X1))) )
| ~ spl22_153
| ~ spl22_265 ),
inference(resolution,[],[f2752,f1396]) ).
fof(f2752,plain,
( ! [X10,X9] :
( ~ in(X9,sK13(X9,X10,X9))
| sP2(X9,X10,X9) )
| ~ spl22_265 ),
inference(avatar_component_clause,[],[f2751]) ).
fof(f39681,plain,
( spl22_1263
| ~ spl22_153
| ~ spl22_262 ),
inference(avatar_split_clause,[],[f2881,f2739,f1395,f39679]) ).
fof(f39679,plain,
( spl22_1263
<=> ! [X2,X0,X1] :
( sP2(X0,apply(X1,X2),apply(X1,X2))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK13(X0,apply(X1,X2),apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1263])]) ).
fof(f2739,plain,
( spl22_262
<=> ! [X9,X10] :
( sP2(X9,X10,X10)
| ~ in(X10,sK13(X9,X10,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_262])]) ).
fof(f2881,plain,
( ! [X2,X0,X1] :
( sP2(X0,apply(X1,X2),apply(X1,X2))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK13(X0,apply(X1,X2),apply(X1,X2))) )
| ~ spl22_153
| ~ spl22_262 ),
inference(resolution,[],[f2740,f1396]) ).
fof(f2740,plain,
( ! [X10,X9] :
( ~ in(X10,sK13(X9,X10,X10))
| sP2(X9,X10,X10) )
| ~ spl22_262 ),
inference(avatar_component_clause,[],[f2739]) ).
fof(f39677,plain,
( spl22_1262
| ~ spl22_78
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2524,f2439,f692,f39675]) ).
fof(f39675,plain,
( spl22_1262
<=> ! [X81,X84,X82,X83] :
( in(sK13(set_intersection2(X81,X82),X83,X84),X81)
| in(sK13(set_intersection2(X81,X82),X83,X84),X84)
| sP2(set_intersection2(X81,X82),X83,X84) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1262])]) ).
fof(f692,plain,
( spl22_78
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_78])]) ).
fof(f2524,plain,
( ! [X82,X83,X81,X84] :
( in(sK13(set_intersection2(X81,X82),X83,X84),X81)
| in(sK13(set_intersection2(X81,X82),X83,X84),X84)
| sP2(set_intersection2(X81,X82),X83,X84) )
| ~ spl22_78
| ~ spl22_238 ),
inference(resolution,[],[f2440,f693]) ).
fof(f693,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2) )
| ~ spl22_78 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f39673,plain,
( spl22_1261
| ~ spl22_170
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2522,f2439,f1550,f39671]) ).
fof(f39671,plain,
( spl22_1261
<=> ! [X73,X75,X76,X74] :
( in(sK13(set_intersection2(X73,X74),X75,X76),X73)
| element(sK13(set_intersection2(X73,X74),X75,X76),X76)
| sP2(set_intersection2(X73,X74),X75,X76) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1261])]) ).
fof(f1550,plain,
( spl22_170
<=> ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X4)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_170])]) ).
fof(f2522,plain,
( ! [X73,X76,X74,X75] :
( in(sK13(set_intersection2(X73,X74),X75,X76),X73)
| element(sK13(set_intersection2(X73,X74),X75,X76),X76)
| sP2(set_intersection2(X73,X74),X75,X76) )
| ~ spl22_170
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1551]) ).
fof(f1551,plain,
( ! [X6,X4,X5] :
( element(sK13(X4,X5,X6),X6)
| in(sK13(X4,X5,X6),X4)
| sP2(X4,X5,X6) )
| ~ spl22_170 ),
inference(avatar_component_clause,[],[f1550]) ).
fof(f39669,plain,
( spl22_1260
| ~ spl22_119
| ~ spl22_906 ),
inference(avatar_split_clause,[],[f18496,f17763,f1078,f39667]) ).
fof(f39667,plain,
( spl22_1260
<=> ! [X8] :
( ~ empty(relation_dom_restriction(sK5,X8))
| sK15 = relation_dom(set_intersection2(relation_dom(sK5),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1260])]) ).
fof(f17763,plain,
( spl22_906
<=> ! [X54] :
( empty(set_intersection2(relation_dom(sK5),X54))
| ~ empty(relation_dom_restriction(sK5,X54)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_906])]) ).
fof(f18496,plain,
( ! [X8] :
( ~ empty(relation_dom_restriction(sK5,X8))
| sK15 = relation_dom(set_intersection2(relation_dom(sK5),X8)) )
| ~ spl22_119
| ~ spl22_906 ),
inference(resolution,[],[f17764,f1079]) ).
fof(f17764,plain,
( ! [X54] :
( empty(set_intersection2(relation_dom(sK5),X54))
| ~ empty(relation_dom_restriction(sK5,X54)) )
| ~ spl22_906 ),
inference(avatar_component_clause,[],[f17763]) ).
fof(f39665,plain,
( spl22_1259
| ~ spl22_77
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2520,f2439,f688,f39663]) ).
fof(f39663,plain,
( spl22_1259
<=> ! [X65,X68,X67,X66] :
( in(sK13(X65,set_intersection2(X66,X67),X68),X66)
| in(sK13(X65,set_intersection2(X66,X67),X68),X68)
| sP2(X65,set_intersection2(X66,X67),X68) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1259])]) ).
fof(f688,plain,
( spl22_77
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_77])]) ).
fof(f2520,plain,
( ! [X65,X68,X66,X67] :
( in(sK13(X65,set_intersection2(X66,X67),X68),X66)
| in(sK13(X65,set_intersection2(X66,X67),X68),X68)
| sP2(X65,set_intersection2(X66,X67),X68) )
| ~ spl22_77
| ~ spl22_238 ),
inference(resolution,[],[f2440,f689]) ).
fof(f689,plain,
( ! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_77 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f39661,plain,
( spl22_1258
| ~ spl22_166
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2518,f2439,f1533,f39659]) ).
fof(f39659,plain,
( spl22_1258
<=> ! [X59,X57,X58,X60] :
( in(sK13(X57,set_intersection2(X58,X59),X60),X58)
| element(sK13(X57,set_intersection2(X58,X59),X60),X60)
| sP2(X57,set_intersection2(X58,X59),X60) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1258])]) ).
fof(f1533,plain,
( spl22_166
<=> ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X5)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_166])]) ).
fof(f2518,plain,
( ! [X58,X59,X57,X60] :
( in(sK13(X57,set_intersection2(X58,X59),X60),X58)
| element(sK13(X57,set_intersection2(X58,X59),X60),X60)
| sP2(X57,set_intersection2(X58,X59),X60) )
| ~ spl22_166
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1534]) ).
fof(f1534,plain,
( ! [X6,X4,X5] :
( element(sK13(X4,X5,X6),X6)
| in(sK13(X4,X5,X6),X5)
| sP2(X4,X5,X6) )
| ~ spl22_166 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f39657,plain,
( spl22_1257
| ~ spl22_172
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2514,f2439,f1558,f39655]) ).
fof(f39655,plain,
( spl22_1257
<=> ! [X41,X42,X44,X43] :
( in(sK13(X41,X42,set_intersection2(X43,X44)),X43)
| element(sK13(X41,X42,set_intersection2(X43,X44)),X41)
| sP2(X41,X42,set_intersection2(X43,X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1257])]) ).
fof(f1558,plain,
( spl22_172
<=> ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X6)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_172])]) ).
fof(f2514,plain,
( ! [X41,X44,X42,X43] :
( in(sK13(X41,X42,set_intersection2(X43,X44)),X43)
| element(sK13(X41,X42,set_intersection2(X43,X44)),X41)
| sP2(X41,X42,set_intersection2(X43,X44)) )
| ~ spl22_172
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1559]) ).
fof(f1559,plain,
( ! [X6,X4,X5] :
( element(sK13(X4,X5,X6),X4)
| in(sK13(X4,X5,X6),X6)
| sP2(X4,X5,X6) )
| ~ spl22_172 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f39653,plain,
( spl22_1256
| ~ spl22_168
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2513,f2439,f1542,f39651]) ).
fof(f39651,plain,
( spl22_1256
<=> ! [X38,X40,X39,X37] :
( in(sK13(X37,X38,set_intersection2(X39,X40)),X39)
| element(sK13(X37,X38,set_intersection2(X39,X40)),X38)
| sP2(X37,X38,set_intersection2(X39,X40)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1256])]) ).
fof(f1542,plain,
( spl22_168
<=> ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X6)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_168])]) ).
fof(f2513,plain,
( ! [X40,X38,X39,X37] :
( in(sK13(X37,X38,set_intersection2(X39,X40)),X39)
| element(sK13(X37,X38,set_intersection2(X39,X40)),X38)
| sP2(X37,X38,set_intersection2(X39,X40)) )
| ~ spl22_168
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1543]) ).
fof(f1543,plain,
( ! [X6,X4,X5] :
( element(sK13(X4,X5,X6),X5)
| in(sK13(X4,X5,X6),X6)
| sP2(X4,X5,X6) )
| ~ spl22_168 ),
inference(avatar_component_clause,[],[f1542]) ).
fof(f39649,plain,
( spl22_1255
| ~ spl22_78
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2510,f2439,f692,f39647]) ).
fof(f39647,plain,
( spl22_1255
<=> ! [X28,X27,X25,X26] :
( in(sK13(X25,X26,set_intersection2(X27,X28)),X27)
| in(sK13(X25,X26,set_intersection2(X27,X28)),X25)
| sP2(X25,X26,set_intersection2(X27,X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1255])]) ).
fof(f2510,plain,
( ! [X28,X26,X27,X25] :
( in(sK13(X25,X26,set_intersection2(X27,X28)),X27)
| in(sK13(X25,X26,set_intersection2(X27,X28)),X25)
| sP2(X25,X26,set_intersection2(X27,X28)) )
| ~ spl22_78
| ~ spl22_238 ),
inference(resolution,[],[f2440,f693]) ).
fof(f39645,plain,
( spl22_1254
| ~ spl22_77
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2509,f2439,f688,f39643]) ).
fof(f39643,plain,
( spl22_1254
<=> ! [X24,X21,X23,X22] :
( in(sK13(X21,X22,set_intersection2(X23,X24)),X23)
| in(sK13(X21,X22,set_intersection2(X23,X24)),X22)
| sP2(X21,X22,set_intersection2(X23,X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1254])]) ).
fof(f2509,plain,
( ! [X21,X24,X22,X23] :
( in(sK13(X21,X22,set_intersection2(X23,X24)),X23)
| in(sK13(X21,X22,set_intersection2(X23,X24)),X22)
| sP2(X21,X22,set_intersection2(X23,X24)) )
| ~ spl22_77
| ~ spl22_238 ),
inference(resolution,[],[f2440,f689]) ).
fof(f39641,plain,
( spl22_1253
| ~ spl22_78
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2493,f2435,f692,f39639]) ).
fof(f39639,plain,
( spl22_1253
<=> ! [X82,X81,X84,X83] :
( in(sK13(set_intersection2(X81,X82),X83,X84),X82)
| in(sK13(set_intersection2(X81,X82),X83,X84),X84)
| sP2(set_intersection2(X81,X82),X83,X84) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1253])]) ).
fof(f2493,plain,
( ! [X82,X83,X81,X84] :
( in(sK13(set_intersection2(X81,X82),X83,X84),X82)
| in(sK13(set_intersection2(X81,X82),X83,X84),X84)
| sP2(set_intersection2(X81,X82),X83,X84) )
| ~ spl22_78
| ~ spl22_237 ),
inference(resolution,[],[f2436,f693]) ).
fof(f39637,plain,
( spl22_1252
| ~ spl22_170
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2491,f2435,f1550,f39635]) ).
fof(f39635,plain,
( spl22_1252
<=> ! [X73,X74,X75,X76] :
( in(sK13(set_intersection2(X73,X74),X75,X76),X74)
| element(sK13(set_intersection2(X73,X74),X75,X76),X76)
| sP2(set_intersection2(X73,X74),X75,X76) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1252])]) ).
fof(f2491,plain,
( ! [X73,X76,X74,X75] :
( in(sK13(set_intersection2(X73,X74),X75,X76),X74)
| element(sK13(set_intersection2(X73,X74),X75,X76),X76)
| sP2(set_intersection2(X73,X74),X75,X76) )
| ~ spl22_170
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1551]) ).
fof(f39633,plain,
( spl22_1251
| ~ spl22_77
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2489,f2435,f688,f39631]) ).
fof(f39631,plain,
( spl22_1251
<=> ! [X66,X68,X67,X65] :
( in(sK13(X65,set_intersection2(X66,X67),X68),X67)
| in(sK13(X65,set_intersection2(X66,X67),X68),X68)
| sP2(X65,set_intersection2(X66,X67),X68) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1251])]) ).
fof(f2489,plain,
( ! [X65,X68,X66,X67] :
( in(sK13(X65,set_intersection2(X66,X67),X68),X67)
| in(sK13(X65,set_intersection2(X66,X67),X68),X68)
| sP2(X65,set_intersection2(X66,X67),X68) )
| ~ spl22_77
| ~ spl22_237 ),
inference(resolution,[],[f2436,f689]) ).
fof(f39629,plain,
( spl22_1250
| ~ spl22_166
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2487,f2435,f1533,f39627]) ).
fof(f39627,plain,
( spl22_1250
<=> ! [X59,X60,X57,X58] :
( in(sK13(X57,set_intersection2(X58,X59),X60),X59)
| element(sK13(X57,set_intersection2(X58,X59),X60),X60)
| sP2(X57,set_intersection2(X58,X59),X60) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1250])]) ).
fof(f2487,plain,
( ! [X58,X59,X57,X60] :
( in(sK13(X57,set_intersection2(X58,X59),X60),X59)
| element(sK13(X57,set_intersection2(X58,X59),X60),X60)
| sP2(X57,set_intersection2(X58,X59),X60) )
| ~ spl22_166
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1534]) ).
fof(f39625,plain,
( spl22_1249
| ~ spl22_118
| ~ spl22_906 ),
inference(avatar_split_clause,[],[f18495,f17763,f1074,f39623]) ).
fof(f39623,plain,
( spl22_1249
<=> ! [X7] :
( ~ empty(relation_dom_restriction(sK5,X7))
| sK15 = relation_rng(set_intersection2(relation_dom(sK5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1249])]) ).
fof(f18495,plain,
( ! [X7] :
( ~ empty(relation_dom_restriction(sK5,X7))
| sK15 = relation_rng(set_intersection2(relation_dom(sK5),X7)) )
| ~ spl22_118
| ~ spl22_906 ),
inference(resolution,[],[f17764,f1075]) ).
fof(f39621,plain,
( spl22_1248
| ~ spl22_172
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2483,f2435,f1558,f39619]) ).
fof(f39619,plain,
( spl22_1248
<=> ! [X41,X42,X44,X43] :
( in(sK13(X41,X42,set_intersection2(X43,X44)),X44)
| element(sK13(X41,X42,set_intersection2(X43,X44)),X41)
| sP2(X41,X42,set_intersection2(X43,X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1248])]) ).
fof(f2483,plain,
( ! [X41,X44,X42,X43] :
( in(sK13(X41,X42,set_intersection2(X43,X44)),X44)
| element(sK13(X41,X42,set_intersection2(X43,X44)),X41)
| sP2(X41,X42,set_intersection2(X43,X44)) )
| ~ spl22_172
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1559]) ).
fof(f39617,plain,
( spl22_1247
| ~ spl22_168
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2482,f2435,f1542,f39615]) ).
fof(f39615,plain,
( spl22_1247
<=> ! [X38,X40,X39,X37] :
( in(sK13(X37,X38,set_intersection2(X39,X40)),X40)
| element(sK13(X37,X38,set_intersection2(X39,X40)),X38)
| sP2(X37,X38,set_intersection2(X39,X40)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1247])]) ).
fof(f2482,plain,
( ! [X40,X38,X39,X37] :
( in(sK13(X37,X38,set_intersection2(X39,X40)),X40)
| element(sK13(X37,X38,set_intersection2(X39,X40)),X38)
| sP2(X37,X38,set_intersection2(X39,X40)) )
| ~ spl22_168
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1543]) ).
fof(f39613,plain,
( spl22_1246
| ~ spl22_78
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2479,f2435,f692,f39611]) ).
fof(f39611,plain,
( spl22_1246
<=> ! [X28,X27,X25,X26] :
( in(sK13(X25,X26,set_intersection2(X27,X28)),X28)
| in(sK13(X25,X26,set_intersection2(X27,X28)),X25)
| sP2(X25,X26,set_intersection2(X27,X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1246])]) ).
fof(f2479,plain,
( ! [X28,X26,X27,X25] :
( in(sK13(X25,X26,set_intersection2(X27,X28)),X28)
| in(sK13(X25,X26,set_intersection2(X27,X28)),X25)
| sP2(X25,X26,set_intersection2(X27,X28)) )
| ~ spl22_78
| ~ spl22_237 ),
inference(resolution,[],[f2436,f693]) ).
fof(f39609,plain,
( spl22_1245
| ~ spl22_77
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2478,f2435,f688,f39607]) ).
fof(f39607,plain,
( spl22_1245
<=> ! [X24,X21,X23,X22] :
( in(sK13(X21,X22,set_intersection2(X23,X24)),X24)
| in(sK13(X21,X22,set_intersection2(X23,X24)),X22)
| sP2(X21,X22,set_intersection2(X23,X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1245])]) ).
fof(f2478,plain,
( ! [X21,X24,X22,X23] :
( in(sK13(X21,X22,set_intersection2(X23,X24)),X24)
| in(sK13(X21,X22,set_intersection2(X23,X24)),X22)
| sP2(X21,X22,set_intersection2(X23,X24)) )
| ~ spl22_77
| ~ spl22_237 ),
inference(resolution,[],[f2436,f689]) ).
fof(f39603,plain,
( spl22_1244
| ~ spl22_647
| ~ spl22_1243 ),
inference(avatar_split_clause,[],[f39599,f39596,f9758,f39601]) ).
fof(f39601,plain,
( spl22_1244
<=> ! [X3] :
( sK15 = X3
| sK15 != relation_dom(X3)
| ~ relation(X3)
| ~ function(X3)
| in(sK12(X3,sK15),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1244])]) ).
fof(f9758,plain,
( spl22_647
<=> ! [X9] : sK15 = relation_dom_restriction(sK15,X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_647])]) ).
fof(f39596,plain,
( spl22_1243
<=> ! [X4,X3] :
( sK15 != relation_dom(X3)
| ~ relation(X3)
| ~ function(X3)
| relation_dom_restriction(sK15,X4) = X3
| in(sK12(X3,sK15),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1243])]) ).
fof(f39599,plain,
( ! [X3] :
( sK15 = X3
| sK15 != relation_dom(X3)
| ~ relation(X3)
| ~ function(X3)
| in(sK12(X3,sK15),sK15) )
| ~ spl22_647
| ~ spl22_1243 ),
inference(forward_demodulation,[],[f39597,f9759]) ).
fof(f9759,plain,
( ! [X9] : sK15 = relation_dom_restriction(sK15,X9)
| ~ spl22_647 ),
inference(avatar_component_clause,[],[f9758]) ).
fof(f39597,plain,
( ! [X3,X4] :
( sK15 != relation_dom(X3)
| ~ relation(X3)
| ~ function(X3)
| relation_dom_restriction(sK15,X4) = X3
| in(sK12(X3,sK15),sK15) )
| ~ spl22_1243 ),
inference(avatar_component_clause,[],[f39596]) ).
fof(f39598,plain,
( ~ spl22_91
| ~ spl22_42
| spl22_1243
| ~ spl22_85
| ~ spl22_112
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1973,f1926,f944,f755,f39596,f433,f795]) ).
fof(f795,plain,
( spl22_91
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_91])]) ).
fof(f433,plain,
( spl22_42
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_42])]) ).
fof(f755,plain,
( spl22_85
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK12(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_85])]) ).
fof(f1926,plain,
( spl22_197
<=> sK15 = relation_dom(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_197])]) ).
fof(f1973,plain,
( ! [X3,X4] :
( sK15 != relation_dom(X3)
| in(sK12(X3,sK15),sK15)
| relation_dom_restriction(sK15,X4) = X3
| ~ function(sK15)
| ~ relation(sK15)
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_85
| ~ spl22_112
| ~ spl22_197 ),
inference(inner_rewriting,[],[f1972]) ).
fof(f1972,plain,
( ! [X3,X4] :
( sK15 != relation_dom(X3)
| in(sK12(X3,sK15),relation_dom(X3))
| relation_dom_restriction(sK15,X4) = X3
| ~ function(sK15)
| ~ relation(sK15)
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_85
| ~ spl22_112
| ~ spl22_197 ),
inference(forward_demodulation,[],[f1960,f945]) ).
fof(f1960,plain,
( ! [X3,X4] :
( relation_dom(X3) != set_intersection2(sK15,X4)
| in(sK12(X3,sK15),relation_dom(X3))
| relation_dom_restriction(sK15,X4) = X3
| ~ function(sK15)
| ~ relation(sK15)
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_85
| ~ spl22_197 ),
inference(superposition,[],[f756,f1928]) ).
fof(f1928,plain,
( sK15 = relation_dom(sK15)
| ~ spl22_197 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f756,plain,
( ! [X2,X0,X1] :
( relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| in(sK12(X1,X2),relation_dom(X1))
| relation_dom_restriction(X2,X0) = X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_85 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f39582,plain,
( spl22_1242
| ~ spl22_708
| ~ spl22_906 ),
inference(avatar_split_clause,[],[f18490,f17763,f10799,f39580]) ).
fof(f39580,plain,
( spl22_1242
<=> ! [X0,X1] :
( ~ empty(relation_dom_restriction(sK5,X0))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1242])]) ).
fof(f10799,plain,
( spl22_708
<=> ! [X6,X7,X8] :
( ~ in(X6,X7)
| ~ in(X6,X8)
| ~ empty(set_intersection2(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_708])]) ).
fof(f18490,plain,
( ! [X0,X1] :
( ~ empty(relation_dom_restriction(sK5,X0))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(sK5)) )
| ~ spl22_708
| ~ spl22_906 ),
inference(resolution,[],[f17764,f10800]) ).
fof(f10800,plain,
( ! [X8,X6,X7] :
( ~ empty(set_intersection2(X7,X8))
| ~ in(X6,X8)
| ~ in(X6,X7) )
| ~ spl22_708 ),
inference(avatar_component_clause,[],[f10799]) ).
fof(f38232,plain,
( spl22_1241
| ~ spl22_124
| ~ spl22_1240 ),
inference(avatar_split_clause,[],[f36946,f35033,f1103,f38230]) ).
fof(f38230,plain,
( spl22_1241
<=> ! [X66] :
( ~ sP0(relation_dom_restriction(sK5,X66),sK15)
| empty(set_intersection2(relation_dom(sK5),X66)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1241])]) ).
fof(f36946,plain,
( ! [X66] :
( ~ sP0(relation_dom_restriction(sK5,X66),sK15)
| empty(set_intersection2(relation_dom(sK5),X66)) )
| ~ spl22_124
| ~ spl22_1240 ),
inference(resolution,[],[f35034,f1104]) ).
fof(f35035,plain,
( spl22_1240
| ~ spl22_236
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15093,f15007,f2331,f35033]) ).
fof(f15093,plain,
( ! [X92,X93] :
( ~ in(X93,set_intersection2(relation_dom(sK5),X92))
| ~ sP0(relation_dom_restriction(sK5,X92),sK15) )
| ~ spl22_236
| ~ spl22_823 ),
inference(superposition,[],[f2332,f15008]) ).
fof(f34020,plain,
( spl22_1239
| ~ spl22_41
| ~ spl22_430 ),
inference(avatar_split_clause,[],[f6035,f6030,f414,f34018]) ).
fof(f34018,plain,
( spl22_1239
<=> ! [X6,X4,X5] :
( apply(sK15,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK15,X4),sK13(X4,X5,X6))
| sP2(X4,X5,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1239])]) ).
fof(f414,plain,
( spl22_41
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_41])]) ).
fof(f6030,plain,
( spl22_430
<=> ! [X20,X18,X19] :
( apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X18),sK13(X18,X19,X20))
| in(sK13(X18,X19,X20),X20)
| sP2(X18,X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_430])]) ).
fof(f6035,plain,
( ! [X6,X4,X5] :
( apply(sK15,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK15,X4),sK13(X4,X5,X6))
| sP2(X4,X5,X6)
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_430 ),
inference(resolution,[],[f6031,f415]) ).
fof(f415,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f6031,plain,
( ! [X18,X19,X20] :
( in(sK13(X18,X19,X20),X20)
| apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X18),sK13(X18,X19,X20))
| sP2(X18,X19,X20) )
| ~ spl22_430 ),
inference(avatar_component_clause,[],[f6030]) ).
fof(f34016,plain,
( spl22_1238
| ~ spl22_41
| ~ spl22_429 ),
inference(avatar_split_clause,[],[f5996,f5991,f414,f34014]) ).
fof(f34014,plain,
( spl22_1238
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK20,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK20,X4),sK13(X4,X5,X6))
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1238])]) ).
fof(f5991,plain,
( spl22_429
<=> ! [X41,X40,X39] :
( sP2(X39,X40,X41)
| in(sK13(X39,X40,X41),X41)
| apply(sK20,sK13(X39,X40,X41)) = apply(relation_dom_restriction(sK20,X39),sK13(X39,X40,X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_429])]) ).
fof(f5996,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK20,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK20,X4),sK13(X4,X5,X6))
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_429 ),
inference(resolution,[],[f5992,f415]) ).
fof(f5992,plain,
( ! [X40,X41,X39] :
( in(sK13(X39,X40,X41),X41)
| sP2(X39,X40,X41)
| apply(sK20,sK13(X39,X40,X41)) = apply(relation_dom_restriction(sK20,X39),sK13(X39,X40,X41)) )
| ~ spl22_429 ),
inference(avatar_component_clause,[],[f5991]) ).
fof(f33972,plain,
( spl22_1237
| ~ spl22_41
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f5959,f5954,f414,f33970]) ).
fof(f33970,plain,
( spl22_1237
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK19,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK19,X4),sK13(X4,X5,X6))
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1237])]) ).
fof(f5954,plain,
( spl22_428
<=> ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| in(sK13(X36,X37,X38),X38)
| apply(sK19,sK13(X36,X37,X38)) = apply(relation_dom_restriction(sK19,X36),sK13(X36,X37,X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_428])]) ).
fof(f5959,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK19,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK19,X4),sK13(X4,X5,X6))
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_428 ),
inference(resolution,[],[f5955,f415]) ).
fof(f5955,plain,
( ! [X38,X36,X37] :
( in(sK13(X36,X37,X38),X38)
| sP2(X36,X37,X38)
| apply(sK19,sK13(X36,X37,X38)) = apply(relation_dom_restriction(sK19,X36),sK13(X36,X37,X38)) )
| ~ spl22_428 ),
inference(avatar_component_clause,[],[f5954]) ).
fof(f33968,plain,
( spl22_1236
| ~ spl22_41
| ~ spl22_427 ),
inference(avatar_split_clause,[],[f5922,f5917,f414,f33966]) ).
fof(f33966,plain,
( spl22_1236
<=> ! [X4,X5,X3] :
( apply(relation_dom_restriction(sK15,X3),sK13(X4,X5,X3)) = apply(sK15,sK13(X4,X5,X3))
| sP2(X4,X5,X3)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1236])]) ).
fof(f5917,plain,
( spl22_427
<=> ! [X20,X18,X19] :
( apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| in(sK13(X18,X19,X20),X18)
| sP2(X18,X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_427])]) ).
fof(f5922,plain,
( ! [X3,X4,X5] :
( apply(relation_dom_restriction(sK15,X3),sK13(X4,X5,X3)) = apply(sK15,sK13(X4,X5,X3))
| sP2(X4,X5,X3)
| ~ empty(X4) )
| ~ spl22_41
| ~ spl22_427 ),
inference(resolution,[],[f5918,f415]) ).
fof(f5918,plain,
( ! [X18,X19,X20] :
( in(sK13(X18,X19,X20),X18)
| apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| sP2(X18,X19,X20) )
| ~ spl22_427 ),
inference(avatar_component_clause,[],[f5917]) ).
fof(f33964,plain,
( spl22_1235
| ~ spl22_41
| ~ spl22_426 ),
inference(avatar_split_clause,[],[f5885,f5880,f414,f33962]) ).
fof(f33962,plain,
( spl22_1235
<=> ! [X4,X5,X3] :
( sP2(X3,X4,X5)
| apply(relation_dom_restriction(sK20,X5),sK13(X3,X4,X5)) = apply(sK20,sK13(X3,X4,X5))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1235])]) ).
fof(f5885,plain,
( ! [X3,X4,X5] :
( sP2(X3,X4,X5)
| apply(relation_dom_restriction(sK20,X5),sK13(X3,X4,X5)) = apply(sK20,sK13(X3,X4,X5))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_426 ),
inference(resolution,[],[f5881,f415]) ).
fof(f33960,plain,
( spl22_1234
| ~ spl22_41
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f5848,f5843,f414,f33958]) ).
fof(f33958,plain,
( spl22_1234
<=> ! [X4,X5,X3] :
( sP2(X3,X4,X5)
| apply(relation_dom_restriction(sK19,X5),sK13(X3,X4,X5)) = apply(sK19,sK13(X3,X4,X5))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1234])]) ).
fof(f5848,plain,
( ! [X3,X4,X5] :
( sP2(X3,X4,X5)
| apply(relation_dom_restriction(sK19,X5),sK13(X3,X4,X5)) = apply(sK19,sK13(X3,X4,X5))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_425 ),
inference(resolution,[],[f5844,f415]) ).
fof(f33956,plain,
( spl22_1233
| ~ spl22_41
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f5806,f5801,f414,f33954]) ).
fof(f33954,plain,
( spl22_1233
<=> ! [X6,X4,X5] :
( apply(sK15,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK15,X5),sK13(X4,X5,X6))
| sP2(X4,X5,X6)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1233])]) ).
fof(f5806,plain,
( ! [X6,X4,X5] :
( apply(sK15,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK15,X5),sK13(X4,X5,X6))
| sP2(X4,X5,X6)
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_423 ),
inference(resolution,[],[f5802,f415]) ).
fof(f33952,plain,
( spl22_1232
| ~ spl22_41
| ~ spl22_422 ),
inference(avatar_split_clause,[],[f5769,f5764,f414,f33950]) ).
fof(f33950,plain,
( spl22_1232
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK20,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK20,X5),sK13(X4,X5,X6))
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1232])]) ).
fof(f5769,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK20,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK20,X5),sK13(X4,X5,X6))
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_422 ),
inference(resolution,[],[f5765,f415]) ).
fof(f33948,plain,
( spl22_1231
| ~ spl22_41
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5732,f5727,f414,f33946]) ).
fof(f33946,plain,
( spl22_1231
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK19,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK19,X5),sK13(X4,X5,X6))
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1231])]) ).
fof(f5732,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(sK19,sK13(X4,X5,X6)) = apply(relation_dom_restriction(sK19,X5),sK13(X4,X5,X6))
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_421 ),
inference(resolution,[],[f5728,f415]) ).
fof(f33944,plain,
( spl22_1230
| ~ spl22_41
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5695,f5690,f414,f33942]) ).
fof(f33942,plain,
( spl22_1230
<=> ! [X6,X4,X5] :
( apply(relation_dom_restriction(sK15,X4),sK13(X5,X6,X4)) = apply(sK15,sK13(X5,X6,X4))
| sP2(X5,X6,X4)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1230])]) ).
fof(f5695,plain,
( ! [X6,X4,X5] :
( apply(relation_dom_restriction(sK15,X4),sK13(X5,X6,X4)) = apply(sK15,sK13(X5,X6,X4))
| sP2(X5,X6,X4)
| ~ empty(X6) )
| ~ spl22_41
| ~ spl22_420 ),
inference(resolution,[],[f5691,f415]) ).
fof(f33940,plain,
( spl22_1229
| ~ spl22_41
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5658,f5653,f414,f33938]) ).
fof(f33938,plain,
( spl22_1229
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(relation_dom_restriction(sK20,X6),sK13(X4,X5,X6)) = apply(sK20,sK13(X4,X5,X6))
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1229])]) ).
fof(f5658,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(relation_dom_restriction(sK20,X6),sK13(X4,X5,X6)) = apply(sK20,sK13(X4,X5,X6))
| ~ empty(X5) )
| ~ spl22_41
| ~ spl22_419 ),
inference(resolution,[],[f5654,f415]) ).
fof(f33936,plain,
( spl22_1228
| ~ spl22_41
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5571,f5566,f414,f33934]) ).
fof(f33934,plain,
( spl22_1228
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(relation_dom_restriction(sK19,X6),sK13(X4,X5,X6)) = apply(sK19,sK13(X4,X5,X6))
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1228])]) ).
fof(f5571,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X6)
| apply(relation_dom_restriction(sK19,X6),sK13(X4,X5,X6)) = apply(sK19,sK13(X4,X5,X6))
| ~ empty(X5) )
| ~ spl22_41
| ~ spl22_418 ),
inference(resolution,[],[f5567,f415]) ).
fof(f33892,plain,
( spl22_1227
| ~ spl22_197
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5221,f5211,f1926,f33890]) ).
fof(f33890,plain,
( spl22_1227
<=> ! [X0] :
( in(sK8(sK15,X0),sK15)
| sP0(sK15,X0)
| apply(relation_dom_restriction(sK15,X0),sK7(sK15,X0)) = apply(sK15,sK7(sK15,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1227])]) ).
fof(f5221,plain,
( ! [X0] :
( in(sK8(sK15,X0),sK15)
| sP0(sK15,X0)
| apply(relation_dom_restriction(sK15,X0),sK7(sK15,X0)) = apply(sK15,sK7(sK15,X0)) )
| ~ spl22_197
| ~ spl22_405 ),
inference(superposition,[],[f5212,f1928]) ).
fof(f33888,plain,
( spl22_1226
| ~ spl22_250
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5215,f5211,f2571,f33886]) ).
fof(f33886,plain,
( spl22_1226
<=> ! [X4,X5,X3] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK15,X4),sK7(X3,X4)) = apply(sK15,sK7(X3,X4))
| ~ sP0(X3,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1226])]) ).
fof(f5215,plain,
( ! [X3,X4,X5] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK15,X4),sK7(X3,X4)) = apply(sK15,sK7(X3,X4))
| ~ sP0(X3,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_405 ),
inference(resolution,[],[f5212,f2572]) ).
fof(f33884,plain,
( spl22_1225
| ~ spl22_250
| ~ spl22_403 ),
inference(avatar_split_clause,[],[f5203,f5195,f2571,f33882]) ).
fof(f33882,plain,
( spl22_1225
<=> ! [X4,X5,X3] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK20,X4),sK7(X3,X4)) = apply(sK20,sK7(X3,X4))
| ~ sP0(X3,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1225])]) ).
fof(f5203,plain,
( ! [X3,X4,X5] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK20,X4),sK7(X3,X4)) = apply(sK20,sK7(X3,X4))
| ~ sP0(X3,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_403 ),
inference(resolution,[],[f5196,f2572]) ).
fof(f33880,plain,
( spl22_1224
| ~ spl22_250
| ~ spl22_402 ),
inference(avatar_split_clause,[],[f5187,f5183,f2571,f33878]) ).
fof(f33878,plain,
( spl22_1224
<=> ! [X4,X5,X3] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK19,X4),sK7(X3,X4)) = apply(sK19,sK7(X3,X4))
| ~ sP0(X3,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1224])]) ).
fof(f5187,plain,
( ! [X3,X4,X5] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK19,X4),sK7(X3,X4)) = apply(sK19,sK7(X3,X4))
| ~ sP0(X3,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_402 ),
inference(resolution,[],[f5184,f2572]) ).
fof(f33876,plain,
( spl22_1223
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_392 ),
inference(avatar_split_clause,[],[f5002,f4946,f812,f249,f433,f33874]) ).
fof(f33874,plain,
( spl22_1223
<=> ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK13(X14,X15,X14)) = apply(sK15,sK13(X14,X15,X14))
| sP2(X14,X15,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1223])]) ).
fof(f249,plain,
( spl22_7
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).
fof(f812,plain,
( spl22_94
<=> empty_set = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_94])]) ).
fof(f4946,plain,
( spl22_392
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X4)
| apply(relation_dom_restriction(X6,X4),sK13(X4,X5,X4)) = apply(X6,sK13(X4,X5,X4))
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_392])]) ).
fof(f5002,plain,
( ! [X14,X15] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X14),sK13(X14,X15,X14)) = apply(sK15,sK13(X14,X15,X14))
| sP2(X14,X15,X14) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_392 ),
inference(forward_demodulation,[],[f5001,f814]) ).
fof(f814,plain,
( empty_set = sK15
| ~ spl22_94 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f5001,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK13(X14,X15,X14)) = apply(sK15,sK13(X14,X15,X14))
| ~ function(empty_set)
| sP2(X14,X15,X14) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_392 ),
inference(forward_demodulation,[],[f4992,f814]) ).
fof(f4992,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(empty_set,X14),sK13(X14,X15,X14)) = apply(empty_set,sK13(X14,X15,X14))
| ~ function(empty_set)
| sP2(X14,X15,X14) )
| ~ spl22_7
| ~ spl22_392 ),
inference(resolution,[],[f4947,f251]) ).
fof(f251,plain,
( relation(empty_set)
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f4947,plain,
( ! [X6,X4,X5] :
( ~ relation(X6)
| apply(relation_dom_restriction(X6,X4),sK13(X4,X5,X4)) = apply(X6,sK13(X4,X5,X4))
| ~ function(X6)
| sP2(X4,X5,X4) )
| ~ spl22_392 ),
inference(avatar_component_clause,[],[f4946]) ).
fof(f33868,plain,
( ~ spl22_20
| spl22_1222
| ~ spl22_19
| ~ spl22_392 ),
inference(avatar_split_clause,[],[f4999,f4946,f309,f33866,f314]) ).
fof(f314,plain,
( spl22_20
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_20])]) ).
fof(f33866,plain,
( spl22_1222
<=> ! [X29,X28] :
( apply(relation_dom_restriction(sK20,X28),sK13(X28,X29,X28)) = apply(sK20,sK13(X28,X29,X28))
| sP2(X28,X29,X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1222])]) ).
fof(f309,plain,
( spl22_19
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_19])]) ).
fof(f4999,plain,
( ! [X28,X29] :
( apply(relation_dom_restriction(sK20,X28),sK13(X28,X29,X28)) = apply(sK20,sK13(X28,X29,X28))
| ~ function(sK20)
| sP2(X28,X29,X28) )
| ~ spl22_19
| ~ spl22_392 ),
inference(resolution,[],[f4947,f311]) ).
fof(f311,plain,
( relation(sK20)
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f33860,plain,
( ~ spl22_18
| spl22_1221
| ~ spl22_17
| ~ spl22_392 ),
inference(avatar_split_clause,[],[f4998,f4946,f299,f33858,f304]) ).
fof(f304,plain,
( spl22_18
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_18])]) ).
fof(f33858,plain,
( spl22_1221
<=> ! [X27,X26] :
( apply(relation_dom_restriction(sK19,X26),sK13(X26,X27,X26)) = apply(sK19,sK13(X26,X27,X26))
| sP2(X26,X27,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1221])]) ).
fof(f299,plain,
( spl22_17
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_17])]) ).
fof(f4998,plain,
( ! [X26,X27] :
( apply(relation_dom_restriction(sK19,X26),sK13(X26,X27,X26)) = apply(sK19,sK13(X26,X27,X26))
| ~ function(sK19)
| sP2(X26,X27,X26) )
| ~ spl22_17
| ~ spl22_392 ),
inference(resolution,[],[f4947,f301]) ).
fof(f301,plain,
( relation(sK19)
| ~ spl22_17 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f33856,plain,
( spl22_1220
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f4983,f4942,f812,f249,f433,f33854]) ).
fof(f33854,plain,
( spl22_1220
<=> ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK13(X15,X14,X14)) = apply(sK15,sK13(X15,X14,X14))
| sP2(X15,X14,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1220])]) ).
fof(f4942,plain,
( spl22_391
<=> ! [X6,X4,X5] :
( sP2(X4,X5,X5)
| apply(relation_dom_restriction(X6,X5),sK13(X4,X5,X5)) = apply(X6,sK13(X4,X5,X5))
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_391])]) ).
fof(f4983,plain,
( ! [X14,X15] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X14),sK13(X15,X14,X14)) = apply(sK15,sK13(X15,X14,X14))
| sP2(X15,X14,X14) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_391 ),
inference(forward_demodulation,[],[f4982,f814]) ).
fof(f4982,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK13(X15,X14,X14)) = apply(sK15,sK13(X15,X14,X14))
| ~ function(empty_set)
| sP2(X15,X14,X14) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_391 ),
inference(forward_demodulation,[],[f4973,f814]) ).
fof(f4973,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(empty_set,X14),sK13(X15,X14,X14)) = apply(empty_set,sK13(X15,X14,X14))
| ~ function(empty_set)
| sP2(X15,X14,X14) )
| ~ spl22_7
| ~ spl22_391 ),
inference(resolution,[],[f4943,f251]) ).
fof(f4943,plain,
( ! [X6,X4,X5] :
( ~ relation(X6)
| apply(relation_dom_restriction(X6,X5),sK13(X4,X5,X5)) = apply(X6,sK13(X4,X5,X5))
| ~ function(X6)
| sP2(X4,X5,X5) )
| ~ spl22_391 ),
inference(avatar_component_clause,[],[f4942]) ).
fof(f33812,plain,
( spl22_1219
| ~ spl22_250
| ~ spl22_379 ),
inference(avatar_split_clause,[],[f4698,f4558,f2571,f33810]) ).
fof(f33810,plain,
( spl22_1219
<=> ! [X35,X34,X33,X32] :
( element(sK13(sK10(powerset(X32)),X33,relation_dom(X34)),X32)
| sP2(sK10(powerset(X32)),X33,relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1219])]) ).
fof(f4698,plain,
( ! [X34,X35,X32,X33] :
( element(sK13(sK10(powerset(X32)),X33,relation_dom(X34)),X32)
| sP2(sK10(powerset(X32)),X33,relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_379 ),
inference(resolution,[],[f4559,f2572]) ).
fof(f33808,plain,
( spl22_1218
| ~ spl22_250
| ~ spl22_378 ),
inference(avatar_split_clause,[],[f4669,f4554,f2571,f33806]) ).
fof(f33806,plain,
( spl22_1218
<=> ! [X35,X34,X33,X32] :
( element(sK13(X32,sK10(powerset(X33)),relation_dom(X34)),X33)
| sP2(X32,sK10(powerset(X33)),relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1218])]) ).
fof(f4669,plain,
( ! [X34,X35,X32,X33] :
( element(sK13(X32,sK10(powerset(X33)),relation_dom(X34)),X33)
| sP2(X32,sK10(powerset(X33)),relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_378 ),
inference(resolution,[],[f4555,f2572]) ).
fof(f33804,plain,
( spl22_1217
| ~ spl22_250
| ~ spl22_377 ),
inference(avatar_split_clause,[],[f4640,f4550,f2571,f33802]) ).
fof(f33802,plain,
( spl22_1217
<=> ! [X35,X34,X33,X32] :
( element(sK13(X32,relation_dom(X33),sK10(powerset(X34))),X34)
| sP2(X32,relation_dom(X33),sK10(powerset(X34)))
| ~ sP0(X33,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1217])]) ).
fof(f4640,plain,
( ! [X34,X35,X32,X33] :
( element(sK13(X32,relation_dom(X33),sK10(powerset(X34))),X34)
| sP2(X32,relation_dom(X33),sK10(powerset(X34)))
| ~ sP0(X33,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_377 ),
inference(resolution,[],[f4551,f2572]) ).
fof(f33800,plain,
( spl22_1216
| ~ spl22_250
| ~ spl22_376 ),
inference(avatar_split_clause,[],[f4611,f4546,f2571,f33798]) ).
fof(f33798,plain,
( spl22_1216
<=> ! [X31,X34,X33,X32] :
( element(sK13(relation_dom(X31),X32,sK10(powerset(X33))),X33)
| sP2(relation_dom(X31),X32,sK10(powerset(X33)))
| ~ sP0(X31,X34)
| ~ empty(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1216])]) ).
fof(f4611,plain,
( ! [X31,X34,X32,X33] :
( element(sK13(relation_dom(X31),X32,sK10(powerset(X33))),X33)
| sP2(relation_dom(X31),X32,sK10(powerset(X33)))
| ~ sP0(X31,X34)
| ~ empty(X34) )
| ~ spl22_250
| ~ spl22_376 ),
inference(resolution,[],[f4547,f2572]) ).
fof(f33796,plain,
( spl22_1215
| ~ spl22_56
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4541,f4168,f540,f33794]) ).
fof(f33794,plain,
( spl22_1215
<=> ! [X13,X12,X11] :
( element(sK13(X11,X12,sK6(X13)),X11)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1215])]) ).
fof(f4541,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,X12,sK6(X13)),X11)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_374 ),
inference(duplicate_literal_removal,[],[f4535]) ).
fof(f4535,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,X12,sK6(X13)),X11)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_374 ),
inference(resolution,[],[f4169,f541]) ).
fof(f33792,plain,
( spl22_1214
| ~ spl22_56
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4450,f4160,f540,f33790]) ).
fof(f33790,plain,
( spl22_1214
<=> ! [X13,X12,X11] :
( element(sK13(sK6(X11),X12,X13),X13)
| sP2(sK6(X11),X12,X13)
| empty(X11)
| in(sK13(sK6(X11),X12,X13),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1214])]) ).
fof(f4450,plain,
( ! [X11,X12,X13] :
( element(sK13(sK6(X11),X12,X13),X13)
| sP2(sK6(X11),X12,X13)
| empty(X11)
| in(sK13(sK6(X11),X12,X13),X11) )
| ~ spl22_56
| ~ spl22_372 ),
inference(duplicate_literal_removal,[],[f4448]) ).
fof(f4448,plain,
( ! [X11,X12,X13] :
( element(sK13(sK6(X11),X12,X13),X13)
| sP2(sK6(X11),X12,X13)
| empty(X11)
| empty(X11)
| in(sK13(sK6(X11),X12,X13),X11) )
| ~ spl22_56
| ~ spl22_372 ),
inference(resolution,[],[f4161,f541]) ).
fof(f33788,plain,
( spl22_1213
| ~ spl22_56
| ~ spl22_370 ),
inference(avatar_split_clause,[],[f4399,f4152,f540,f33786]) ).
fof(f33786,plain,
( spl22_1213
<=> ! [X13,X12,X11] :
( element(sK13(X11,X12,sK6(X13)),X12)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1213])]) ).
fof(f4399,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,X12,sK6(X13)),X12)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_370 ),
inference(duplicate_literal_removal,[],[f4393]) ).
fof(f4393,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,X12,sK6(X13)),X12)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_370 ),
inference(resolution,[],[f4153,f541]) ).
fof(f33784,plain,
( spl22_1212
| ~ spl22_56
| ~ spl22_368 ),
inference(avatar_split_clause,[],[f4348,f4144,f540,f33782]) ).
fof(f33782,plain,
( spl22_1212
<=> ! [X13,X12,X11] :
( element(sK13(X11,sK6(X12),X13),X13)
| sP2(X11,sK6(X12),X13)
| empty(X12)
| in(sK13(X11,sK6(X12),X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1212])]) ).
fof(f4348,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK6(X12),X13),X13)
| sP2(X11,sK6(X12),X13)
| empty(X12)
| in(sK13(X11,sK6(X12),X13),X12) )
| ~ spl22_56
| ~ spl22_368 ),
inference(duplicate_literal_removal,[],[f4346]) ).
fof(f4346,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK6(X12),X13),X13)
| sP2(X11,sK6(X12),X13)
| empty(X12)
| empty(X12)
| in(sK13(X11,sK6(X12),X13),X12) )
| ~ spl22_56
| ~ spl22_368 ),
inference(resolution,[],[f4145,f541]) ).
fof(f33780,plain,
( spl22_1211
| ~ spl22_56
| ~ spl22_365 ),
inference(avatar_split_clause,[],[f4278,f4131,f540,f33778]) ).
fof(f33778,plain,
( spl22_1211
<=> ! [X13,X12,X11] :
( in(sK13(sK6(X11),X12,X13),X13)
| empty(X11)
| sP2(sK6(X11),X12,X13)
| in(sK13(sK6(X11),X12,X13),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1211])]) ).
fof(f4278,plain,
( ! [X11,X12,X13] :
( in(sK13(sK6(X11),X12,X13),X13)
| empty(X11)
| sP2(sK6(X11),X12,X13)
| in(sK13(sK6(X11),X12,X13),X11) )
| ~ spl22_56
| ~ spl22_365 ),
inference(duplicate_literal_removal,[],[f4256]) ).
fof(f4256,plain,
( ! [X11,X12,X13] :
( in(sK13(sK6(X11),X12,X13),X13)
| empty(X11)
| sP2(sK6(X11),X12,X13)
| empty(X11)
| in(sK13(sK6(X11),X12,X13),X11) )
| ~ spl22_56
| ~ spl22_365 ),
inference(resolution,[],[f4132,f541]) ).
fof(f33776,plain,
( spl22_1210
| ~ spl22_250
| ~ spl22_365 ),
inference(avatar_split_clause,[],[f4267,f4131,f2571,f33774]) ).
fof(f33774,plain,
( spl22_1210
<=> ! [X35,X34,X33,X32] :
( element(sK13(sK6(X32),X33,relation_dom(X34)),X32)
| empty(X32)
| sP2(sK6(X32),X33,relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1210])]) ).
fof(f4267,plain,
( ! [X34,X35,X32,X33] :
( element(sK13(sK6(X32),X33,relation_dom(X34)),X32)
| empty(X32)
| sP2(sK6(X32),X33,relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_365 ),
inference(resolution,[],[f4132,f2572]) ).
fof(f33732,plain,
( spl22_1209
| ~ spl22_45
| ~ spl22_365 ),
inference(avatar_split_clause,[],[f4262,f4131,f448,f33730]) ).
fof(f33730,plain,
( spl22_1209
<=> ! [X16,X14,X15] :
( element(sK13(sK6(X14),X15,X16),X14)
| empty(X14)
| sP2(sK6(X14),X15,X16)
| ~ in(X16,sK13(sK6(X14),X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1209])]) ).
fof(f4262,plain,
( ! [X16,X14,X15] :
( element(sK13(sK6(X14),X15,X16),X14)
| empty(X14)
| sP2(sK6(X14),X15,X16)
| ~ in(X16,sK13(sK6(X14),X15,X16)) )
| ~ spl22_45
| ~ spl22_365 ),
inference(resolution,[],[f4132,f449]) ).
fof(f33728,plain,
( spl22_1208
| ~ spl22_56
| ~ spl22_364 ),
inference(avatar_split_clause,[],[f4252,f4127,f540,f33726]) ).
fof(f33726,plain,
( spl22_1208
<=> ! [X13,X12,X11] :
( in(sK13(X11,sK6(X12),X13),X13)
| empty(X12)
| sP2(X11,sK6(X12),X13)
| in(sK13(X11,sK6(X12),X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1208])]) ).
fof(f4252,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,sK6(X12),X13),X13)
| empty(X12)
| sP2(X11,sK6(X12),X13)
| in(sK13(X11,sK6(X12),X13),X12) )
| ~ spl22_56
| ~ spl22_364 ),
inference(duplicate_literal_removal,[],[f4230]) ).
fof(f4230,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,sK6(X12),X13),X13)
| empty(X12)
| sP2(X11,sK6(X12),X13)
| empty(X12)
| in(sK13(X11,sK6(X12),X13),X12) )
| ~ spl22_56
| ~ spl22_364 ),
inference(resolution,[],[f4128,f541]) ).
fof(f33724,plain,
( spl22_1207
| ~ spl22_250
| ~ spl22_364 ),
inference(avatar_split_clause,[],[f4241,f4127,f2571,f33722]) ).
fof(f33722,plain,
( spl22_1207
<=> ! [X35,X34,X33,X32] :
( element(sK13(X32,sK6(X33),relation_dom(X34)),X33)
| empty(X33)
| sP2(X32,sK6(X33),relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1207])]) ).
fof(f4241,plain,
( ! [X34,X35,X32,X33] :
( element(sK13(X32,sK6(X33),relation_dom(X34)),X33)
| empty(X33)
| sP2(X32,sK6(X33),relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_364 ),
inference(resolution,[],[f4128,f2572]) ).
fof(f33720,plain,
( spl22_1206
| ~ spl22_45
| ~ spl22_364 ),
inference(avatar_split_clause,[],[f4236,f4127,f448,f33718]) ).
fof(f33718,plain,
( spl22_1206
<=> ! [X16,X14,X15] :
( element(sK13(X14,sK6(X15),X16),X15)
| empty(X15)
| sP2(X14,sK6(X15),X16)
| ~ in(X16,sK13(X14,sK6(X15),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1206])]) ).
fof(f4236,plain,
( ! [X16,X14,X15] :
( element(sK13(X14,sK6(X15),X16),X15)
| empty(X15)
| sP2(X14,sK6(X15),X16)
| ~ in(X16,sK13(X14,sK6(X15),X16)) )
| ~ spl22_45
| ~ spl22_364 ),
inference(resolution,[],[f4128,f449]) ).
fof(f33716,plain,
( spl22_1205
| ~ spl22_56
| ~ spl22_363 ),
inference(avatar_split_clause,[],[f4226,f4123,f540,f33714]) ).
fof(f33714,plain,
( spl22_1205
<=> ! [X13,X12,X11] :
( in(sK13(X11,X12,sK6(X13)),X12)
| empty(X13)
| sP2(X11,X12,sK6(X13))
| in(sK13(X11,X12,sK6(X13)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1205])]) ).
fof(f4226,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,X12,sK6(X13)),X12)
| empty(X13)
| sP2(X11,X12,sK6(X13))
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_363 ),
inference(duplicate_literal_removal,[],[f4204]) ).
fof(f4204,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,X12,sK6(X13)),X12)
| empty(X13)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_363 ),
inference(resolution,[],[f4124,f541]) ).
fof(f33712,plain,
( spl22_1204
| ~ spl22_250
| ~ spl22_363 ),
inference(avatar_split_clause,[],[f4215,f4123,f2571,f33710]) ).
fof(f33710,plain,
( spl22_1204
<=> ! [X35,X34,X33,X32] :
( element(sK13(X32,relation_dom(X33),sK6(X34)),X34)
| empty(X34)
| sP2(X32,relation_dom(X33),sK6(X34))
| ~ sP0(X33,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1204])]) ).
fof(f4215,plain,
( ! [X34,X35,X32,X33] :
( element(sK13(X32,relation_dom(X33),sK6(X34)),X34)
| empty(X34)
| sP2(X32,relation_dom(X33),sK6(X34))
| ~ sP0(X33,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_363 ),
inference(resolution,[],[f4124,f2572]) ).
fof(f33708,plain,
( spl22_1203
| ~ spl22_45
| ~ spl22_363 ),
inference(avatar_split_clause,[],[f4210,f4123,f448,f33706]) ).
fof(f33706,plain,
( spl22_1203
<=> ! [X16,X14,X15] :
( element(sK13(X14,X15,sK6(X16)),X16)
| empty(X16)
| sP2(X14,X15,sK6(X16))
| ~ in(X15,sK13(X14,X15,sK6(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1203])]) ).
fof(f4210,plain,
( ! [X16,X14,X15] :
( element(sK13(X14,X15,sK6(X16)),X16)
| empty(X16)
| sP2(X14,X15,sK6(X16))
| ~ in(X15,sK13(X14,X15,sK6(X16))) )
| ~ spl22_45
| ~ spl22_363 ),
inference(resolution,[],[f4124,f449]) ).
fof(f33704,plain,
( spl22_1202
| ~ spl22_56
| ~ spl22_362 ),
inference(avatar_split_clause,[],[f4200,f4119,f540,f33702]) ).
fof(f33702,plain,
( spl22_1202
<=> ! [X13,X12,X11] :
( in(sK13(X11,X12,sK6(X13)),X11)
| empty(X13)
| sP2(X11,X12,sK6(X13))
| in(sK13(X11,X12,sK6(X13)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1202])]) ).
fof(f4200,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,X12,sK6(X13)),X11)
| empty(X13)
| sP2(X11,X12,sK6(X13))
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_362 ),
inference(duplicate_literal_removal,[],[f4178]) ).
fof(f4178,plain,
( ! [X11,X12,X13] :
( in(sK13(X11,X12,sK6(X13)),X11)
| empty(X13)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_362 ),
inference(resolution,[],[f4120,f541]) ).
fof(f33700,plain,
( spl22_1201
| ~ spl22_250
| ~ spl22_362 ),
inference(avatar_split_clause,[],[f4189,f4119,f2571,f33698]) ).
fof(f33698,plain,
( spl22_1201
<=> ! [X31,X34,X33,X32] :
( element(sK13(relation_dom(X31),X32,sK6(X33)),X33)
| empty(X33)
| sP2(relation_dom(X31),X32,sK6(X33))
| ~ sP0(X31,X34)
| ~ empty(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1201])]) ).
fof(f4189,plain,
( ! [X31,X34,X32,X33] :
( element(sK13(relation_dom(X31),X32,sK6(X33)),X33)
| empty(X33)
| sP2(relation_dom(X31),X32,sK6(X33))
| ~ sP0(X31,X34)
| ~ empty(X34) )
| ~ spl22_250
| ~ spl22_362 ),
inference(resolution,[],[f4120,f2572]) ).
fof(f33696,plain,
( spl22_1200
| ~ spl22_45
| ~ spl22_362 ),
inference(avatar_split_clause,[],[f4184,f4119,f448,f33694]) ).
fof(f33694,plain,
( spl22_1200
<=> ! [X13,X14,X15] :
( element(sK13(X13,X14,sK6(X15)),X15)
| empty(X15)
| sP2(X13,X14,sK6(X15))
| ~ in(X13,sK13(X13,X14,sK6(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1200])]) ).
fof(f4184,plain,
( ! [X14,X15,X13] :
( element(sK13(X13,X14,sK6(X15)),X15)
| empty(X15)
| sP2(X13,X14,sK6(X15))
| ~ in(X13,sK13(X13,X14,sK6(X15))) )
| ~ spl22_45
| ~ spl22_362 ),
inference(resolution,[],[f4120,f449]) ).
fof(f33692,plain,
( spl22_1199
| spl22_81
| ~ spl22_936 ),
inference(avatar_split_clause,[],[f18328,f18244,f730,f33689]) ).
fof(f33689,plain,
( spl22_1199
<=> apply(relation_dom_restriction(sK20,sK5),sK10(sK5)) = apply(sK20,sK10(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1199])]) ).
fof(f730,plain,
( spl22_81
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_81])]) ).
fof(f18244,plain,
( spl22_936
<=> ! [X17] :
( apply(relation_dom_restriction(sK20,X17),sK10(X17)) = apply(sK20,sK10(X17))
| empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_936])]) ).
fof(f18328,plain,
( apply(relation_dom_restriction(sK20,sK5),sK10(sK5)) = apply(sK20,sK10(sK5))
| spl22_81
| ~ spl22_936 ),
inference(resolution,[],[f18245,f732]) ).
fof(f732,plain,
( ~ empty(sK5)
| spl22_81 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f18245,plain,
( ! [X17] :
( empty(X17)
| apply(relation_dom_restriction(sK20,X17),sK10(X17)) = apply(sK20,sK10(X17)) )
| ~ spl22_936 ),
inference(avatar_component_clause,[],[f18244]) ).
fof(f33687,plain,
( spl22_1198
| ~ spl22_67
| ~ spl22_337 ),
inference(avatar_split_clause,[],[f3736,f3449,f633,f33685]) ).
fof(f33685,plain,
( spl22_1198
<=> ! [X5,X4,X7,X6] :
( sP2(powerset(X4),X5,sK10(powerset(X6)))
| ~ empty(X6)
| element(X7,X4)
| ~ in(X7,sK13(powerset(X4),X5,sK10(powerset(X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1198])]) ).
fof(f3449,plain,
( spl22_337
<=> ! [X22,X24,X23] :
( element(sK13(X22,X23,sK10(powerset(X24))),X22)
| sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_337])]) ).
fof(f3736,plain,
( ! [X6,X7,X4,X5] :
( sP2(powerset(X4),X5,sK10(powerset(X6)))
| ~ empty(X6)
| element(X7,X4)
| ~ in(X7,sK13(powerset(X4),X5,sK10(powerset(X6)))) )
| ~ spl22_67
| ~ spl22_337 ),
inference(resolution,[],[f3450,f634]) ).
fof(f3450,plain,
( ! [X24,X22,X23] :
( element(sK13(X22,X23,sK10(powerset(X24))),X22)
| sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X24) )
| ~ spl22_337 ),
inference(avatar_component_clause,[],[f3449]) ).
fof(f33683,plain,
( spl22_1197
| ~ spl22_67
| ~ spl22_335 ),
inference(avatar_split_clause,[],[f3731,f3441,f633,f33681]) ).
fof(f33681,plain,
( spl22_1197
<=> ! [X5,X4,X7,X6] :
( sP2(sK10(powerset(X4)),X5,powerset(X6))
| ~ empty(X4)
| element(X7,X6)
| ~ in(X7,sK13(sK10(powerset(X4)),X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1197])]) ).
fof(f3441,plain,
( spl22_335
<=> ! [X22,X21,X23] :
( element(sK13(sK10(powerset(X21)),X22,X23),X23)
| sP2(sK10(powerset(X21)),X22,X23)
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_335])]) ).
fof(f3731,plain,
( ! [X6,X7,X4,X5] :
( sP2(sK10(powerset(X4)),X5,powerset(X6))
| ~ empty(X4)
| element(X7,X6)
| ~ in(X7,sK13(sK10(powerset(X4)),X5,powerset(X6))) )
| ~ spl22_67
| ~ spl22_335 ),
inference(resolution,[],[f3442,f634]) ).
fof(f3442,plain,
( ! [X21,X22,X23] :
( element(sK13(sK10(powerset(X21)),X22,X23),X23)
| sP2(sK10(powerset(X21)),X22,X23)
| ~ empty(X21) )
| ~ spl22_335 ),
inference(avatar_component_clause,[],[f3441]) ).
fof(f33679,plain,
( spl22_1196
| ~ spl22_65
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f3724,f3433,f610,f33677]) ).
fof(f33677,plain,
( spl22_1196
<=> ! [X2,X0,X1,X3] :
( element(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1196])]) ).
fof(f3724,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) )
| ~ spl22_65
| ~ spl22_333 ),
inference(resolution,[],[f3434,f611]) ).
fof(f33675,plain,
( spl22_1195
| ~ spl22_65
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f3720,f3433,f610,f33673]) ).
fof(f33673,plain,
( spl22_1195
<=> ! [X2,X0,X1,X3] :
( element(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1195])]) ).
fof(f3720,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_333 ),
inference(resolution,[],[f3434,f611]) ).
fof(f33671,plain,
( spl22_1194
| ~ spl22_67
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f3713,f3429,f633,f33669]) ).
fof(f33669,plain,
( spl22_1194
<=> ! [X5,X4,X7,X6] :
( sP2(X4,powerset(X5),sK10(powerset(X6)))
| ~ empty(X6)
| element(X7,X5)
| ~ in(X7,sK13(X4,powerset(X5),sK10(powerset(X6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1194])]) ).
fof(f3429,plain,
( spl22_332
<=> ! [X24,X22,X23] :
( element(sK13(X22,X23,sK10(powerset(X24))),X23)
| sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_332])]) ).
fof(f3713,plain,
( ! [X6,X7,X4,X5] :
( sP2(X4,powerset(X5),sK10(powerset(X6)))
| ~ empty(X6)
| element(X7,X5)
| ~ in(X7,sK13(X4,powerset(X5),sK10(powerset(X6)))) )
| ~ spl22_67
| ~ spl22_332 ),
inference(resolution,[],[f3430,f634]) ).
fof(f3430,plain,
( ! [X24,X22,X23] :
( element(sK13(X22,X23,sK10(powerset(X24))),X23)
| sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X24) )
| ~ spl22_332 ),
inference(avatar_component_clause,[],[f3429]) ).
fof(f33667,plain,
( spl22_1193
| ~ spl22_67
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f3708,f3421,f633,f33665]) ).
fof(f33665,plain,
( spl22_1193
<=> ! [X5,X4,X7,X6] :
( sP2(X4,sK10(powerset(X5)),powerset(X6))
| ~ empty(X5)
| element(X7,X6)
| ~ in(X7,sK13(X4,sK10(powerset(X5)),powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1193])]) ).
fof(f3421,plain,
( spl22_330
<=> ! [X22,X21,X23] :
( element(sK13(X21,sK10(powerset(X22)),X23),X23)
| sP2(X21,sK10(powerset(X22)),X23)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_330])]) ).
fof(f3708,plain,
( ! [X6,X7,X4,X5] :
( sP2(X4,sK10(powerset(X5)),powerset(X6))
| ~ empty(X5)
| element(X7,X6)
| ~ in(X7,sK13(X4,sK10(powerset(X5)),powerset(X6))) )
| ~ spl22_67
| ~ spl22_330 ),
inference(resolution,[],[f3422,f634]) ).
fof(f3422,plain,
( ! [X21,X22,X23] :
( element(sK13(X21,sK10(powerset(X22)),X23),X23)
| sP2(X21,sK10(powerset(X22)),X23)
| ~ empty(X22) )
| ~ spl22_330 ),
inference(avatar_component_clause,[],[f3421]) ).
fof(f33663,plain,
( spl22_1192
| ~ spl22_65
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3701,f3396,f610,f33661]) ).
fof(f33661,plain,
( spl22_1192
<=> ! [X2,X0,X1,X3] :
( element(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1192])]) ).
fof(f3701,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) )
| ~ spl22_65
| ~ spl22_328 ),
inference(resolution,[],[f3397,f611]) ).
fof(f33659,plain,
( spl22_1191
| ~ spl22_65
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3697,f3396,f610,f33657]) ).
fof(f33657,plain,
( spl22_1191
<=> ! [X2,X0,X1,X3] :
( element(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1191])]) ).
fof(f3697,plain,
( ! [X2,X3,X0,X1] :
( element(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_328 ),
inference(resolution,[],[f3397,f611]) ).
fof(f33655,plain,
( spl22_1190
| ~ spl22_67
| ~ spl22_327 ),
inference(avatar_split_clause,[],[f3694,f3392,f633,f33653]) ).
fof(f33653,plain,
( spl22_1190
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X4,X5,sK10(powerset(powerset(X6))))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,sK10(powerset(powerset(X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1190])]) ).
fof(f3392,plain,
( spl22_327
<=> ! [X20,X21,X19] :
( sP2(X19,X20,sK10(powerset(X21)))
| ~ empty(X19)
| element(sK13(X19,X20,sK10(powerset(X21))),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_327])]) ).
fof(f3694,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X4,X5,sK10(powerset(powerset(X6))))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,sK10(powerset(powerset(X6))))) )
| ~ spl22_67
| ~ spl22_327 ),
inference(resolution,[],[f3393,f634]) ).
fof(f3393,plain,
( ! [X21,X19,X20] :
( element(sK13(X19,X20,sK10(powerset(X21))),X21)
| ~ empty(X19)
| sP2(X19,X20,sK10(powerset(X21))) )
| ~ spl22_327 ),
inference(avatar_component_clause,[],[f3392]) ).
fof(f33651,plain,
( spl22_1189
| ~ spl22_65
| ~ spl22_326 ),
inference(avatar_split_clause,[],[f3688,f3388,f610,f33649]) ).
fof(f33649,plain,
( spl22_1189
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X0,X1,sK6(powerset(X2)))
| empty(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,sK6(powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1189])]) ).
fof(f3688,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK6(powerset(X2)))
| empty(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,sK6(powerset(X2)))) )
| ~ spl22_65
| ~ spl22_326 ),
inference(resolution,[],[f3389,f611]) ).
fof(f33647,plain,
( spl22_1188
| spl22_47
| ~ spl22_936 ),
inference(avatar_split_clause,[],[f18327,f18244,f475,f33644]) ).
fof(f33644,plain,
( spl22_1188
<=> apply(relation_dom_restriction(sK20,sK3),sK10(sK3)) = apply(sK20,sK10(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1188])]) ).
fof(f475,plain,
( spl22_47
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_47])]) ).
fof(f18327,plain,
( apply(relation_dom_restriction(sK20,sK3),sK10(sK3)) = apply(sK20,sK10(sK3))
| spl22_47
| ~ spl22_936 ),
inference(resolution,[],[f18245,f477]) ).
fof(f477,plain,
( ~ empty(sK3)
| spl22_47 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f33642,plain,
( spl22_1187
| ~ spl22_67
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3685,f3384,f633,f33640]) ).
fof(f33640,plain,
( spl22_1187
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(sK10(powerset(powerset(X5))),X6,X4)
| element(X7,X5)
| ~ in(X7,sK13(sK10(powerset(powerset(X5))),X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1187])]) ).
fof(f3384,plain,
( spl22_325
<=> ! [X20,X18,X19] :
( sP2(sK10(powerset(X18)),X19,X20)
| ~ empty(X20)
| element(sK13(sK10(powerset(X18)),X19,X20),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_325])]) ).
fof(f3685,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(sK10(powerset(powerset(X5))),X6,X4)
| element(X7,X5)
| ~ in(X7,sK13(sK10(powerset(powerset(X5))),X6,X4)) )
| ~ spl22_67
| ~ spl22_325 ),
inference(resolution,[],[f3385,f634]) ).
fof(f3385,plain,
( ! [X18,X19,X20] :
( element(sK13(sK10(powerset(X18)),X19,X20),X18)
| ~ empty(X20)
| sP2(sK10(powerset(X18)),X19,X20) )
| ~ spl22_325 ),
inference(avatar_component_clause,[],[f3384]) ).
fof(f33638,plain,
( spl22_1186
| ~ spl22_65
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3679,f3380,f610,f33636]) ).
fof(f33636,plain,
( spl22_1186
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(sK6(powerset(X1)),X2,X0)
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X3,sK13(sK6(powerset(X1)),X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1186])]) ).
fof(f3679,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(sK6(powerset(X1)),X2,X0)
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X3,sK13(sK6(powerset(X1)),X2,X0)) )
| ~ spl22_65
| ~ spl22_324 ),
inference(resolution,[],[f3381,f611]) ).
fof(f33634,plain,
( spl22_1185
| ~ spl22_67
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3676,f3376,f633,f33632]) ).
fof(f33632,plain,
( spl22_1185
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X5,X4,sK10(powerset(powerset(X6))))
| element(X7,X6)
| ~ in(X7,sK13(X5,X4,sK10(powerset(powerset(X6))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1185])]) ).
fof(f3376,plain,
( spl22_323
<=> ! [X20,X21,X19] :
( sP2(X19,X20,sK10(powerset(X21)))
| ~ empty(X20)
| element(sK13(X19,X20,sK10(powerset(X21))),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_323])]) ).
fof(f3676,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X5,X4,sK10(powerset(powerset(X6))))
| element(X7,X6)
| ~ in(X7,sK13(X5,X4,sK10(powerset(powerset(X6))))) )
| ~ spl22_67
| ~ spl22_323 ),
inference(resolution,[],[f3377,f634]) ).
fof(f3377,plain,
( ! [X21,X19,X20] :
( element(sK13(X19,X20,sK10(powerset(X21))),X21)
| ~ empty(X20)
| sP2(X19,X20,sK10(powerset(X21))) )
| ~ spl22_323 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f33630,plain,
( spl22_1184
| ~ spl22_65
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3662,f3372,f610,f33628]) ).
fof(f33628,plain,
( spl22_1184
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,X0,sK6(powerset(X2)))
| empty(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,sK6(powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1184])]) ).
fof(f3662,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK6(powerset(X2)))
| empty(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,sK6(powerset(X2)))) )
| ~ spl22_65
| ~ spl22_322 ),
inference(resolution,[],[f3373,f611]) ).
fof(f33626,plain,
( spl22_1183
| ~ spl22_67
| ~ spl22_321 ),
inference(avatar_split_clause,[],[f3659,f3368,f633,f33624]) ).
fof(f33624,plain,
( spl22_1183
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X5,sK10(powerset(powerset(X6))),X4)
| element(X7,X6)
| ~ in(X7,sK13(X5,sK10(powerset(powerset(X6))),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1183])]) ).
fof(f3368,plain,
( spl22_321
<=> ! [X20,X18,X19] :
( sP2(X18,sK10(powerset(X19)),X20)
| ~ empty(X20)
| element(sK13(X18,sK10(powerset(X19)),X20),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_321])]) ).
fof(f3659,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X5,sK10(powerset(powerset(X6))),X4)
| element(X7,X6)
| ~ in(X7,sK13(X5,sK10(powerset(powerset(X6))),X4)) )
| ~ spl22_67
| ~ spl22_321 ),
inference(resolution,[],[f3369,f634]) ).
fof(f3369,plain,
( ! [X18,X19,X20] :
( element(sK13(X18,sK10(powerset(X19)),X20),X19)
| ~ empty(X20)
| sP2(X18,sK10(powerset(X19)),X20) )
| ~ spl22_321 ),
inference(avatar_component_clause,[],[f3368]) ).
fof(f33622,plain,
( spl22_1182
| ~ spl22_65
| ~ spl22_320 ),
inference(avatar_split_clause,[],[f3653,f3364,f610,f33620]) ).
fof(f33620,plain,
( spl22_1182
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,sK6(powerset(X2)),X0)
| empty(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,sK6(powerset(X2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1182])]) ).
fof(f3653,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK6(powerset(X2)),X0)
| empty(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,sK6(powerset(X2)),X0)) )
| ~ spl22_65
| ~ spl22_320 ),
inference(resolution,[],[f3365,f611]) ).
fof(f33618,plain,
( spl22_1181
| ~ spl22_52
| ~ spl22_318 ),
inference(avatar_split_clause,[],[f3599,f3339,f498,f33616]) ).
fof(f33616,plain,
( spl22_1181
<=> ! [X6,X7] :
( sP2(sK6(powerset(X6)),X7,sK6(powerset(X6)))
| empty(powerset(X6))
| subset(sK13(sK6(powerset(X6)),X7,sK6(powerset(X6))),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1181])]) ).
fof(f3599,plain,
( ! [X6,X7] :
( sP2(sK6(powerset(X6)),X7,sK6(powerset(X6)))
| empty(powerset(X6))
| subset(sK13(sK6(powerset(X6)),X7,sK6(powerset(X6))),X6) )
| ~ spl22_52
| ~ spl22_318 ),
inference(resolution,[],[f3340,f499]) ).
fof(f33614,plain,
( spl22_1180
| ~ spl22_52
| ~ spl22_316 ),
inference(avatar_split_clause,[],[f3543,f3331,f498,f33612]) ).
fof(f33612,plain,
( spl22_1180
<=> ! [X6,X7] :
( sP2(X6,sK6(powerset(X7)),sK6(powerset(X7)))
| empty(powerset(X7))
| subset(sK13(X6,sK6(powerset(X7)),sK6(powerset(X7))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1180])]) ).
fof(f3543,plain,
( ! [X6,X7] :
( sP2(X6,sK6(powerset(X7)),sK6(powerset(X7)))
| empty(powerset(X7))
| subset(sK13(X6,sK6(powerset(X7)),sK6(powerset(X7))),X7) )
| ~ spl22_52
| ~ spl22_316 ),
inference(resolution,[],[f3332,f499]) ).
fof(f33610,plain,
( spl22_1179
| ~ spl22_67
| ~ spl22_307 ),
inference(avatar_split_clause,[],[f3284,f3260,f633,f33608]) ).
fof(f33608,plain,
( spl22_1179
<=> ! [X4,X5,X3] :
( ~ empty(relation_dom(X3))
| sP0(X3,sK6(powerset(X4)))
| empty(powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,sK6(powerset(X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1179])]) ).
fof(f3260,plain,
( spl22_307
<=> ! [X9,X10] :
( sP0(X9,sK6(X10))
| ~ empty(relation_dom(X9))
| element(sK7(X9,sK6(X10)),X10)
| empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_307])]) ).
fof(f3284,plain,
( ! [X3,X4,X5] :
( ~ empty(relation_dom(X3))
| sP0(X3,sK6(powerset(X4)))
| empty(powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,sK6(powerset(X4)))) )
| ~ spl22_67
| ~ spl22_307 ),
inference(resolution,[],[f3261,f634]) ).
fof(f3261,plain,
( ! [X10,X9] :
( element(sK7(X9,sK6(X10)),X10)
| ~ empty(relation_dom(X9))
| sP0(X9,sK6(X10))
| empty(X10) )
| ~ spl22_307 ),
inference(avatar_component_clause,[],[f3260]) ).
fof(f33606,plain,
( spl22_1178
| ~ spl22_153
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3192,f3185,f1395,f33604]) ).
fof(f33604,plain,
( spl22_1178
<=> ! [X2,X0,X1] :
( ~ sP1(X0)
| apply(X1,X2) = apply(X0,sK9(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1178])]) ).
fof(f3192,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0)
| apply(X1,X2) = apply(X0,sK9(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,relation_rng(X0)) )
| ~ spl22_153
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1396]) ).
fof(f33602,plain,
( spl22_1177
| spl22_81
| ~ spl22_934 ),
inference(avatar_split_clause,[],[f18233,f18149,f730,f33599]) ).
fof(f33599,plain,
( spl22_1177
<=> apply(relation_dom_restriction(sK19,sK5),sK10(sK5)) = apply(sK19,sK10(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1177])]) ).
fof(f18149,plain,
( spl22_934
<=> ! [X16] :
( apply(relation_dom_restriction(sK19,X16),sK10(X16)) = apply(sK19,sK10(X16))
| empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_934])]) ).
fof(f18233,plain,
( apply(relation_dom_restriction(sK19,sK5),sK10(sK5)) = apply(sK19,sK10(sK5))
| spl22_81
| ~ spl22_934 ),
inference(resolution,[],[f18150,f732]) ).
fof(f18150,plain,
( ! [X16] :
( empty(X16)
| apply(relation_dom_restriction(sK19,X16),sK10(X16)) = apply(sK19,sK10(X16)) )
| ~ spl22_934 ),
inference(avatar_component_clause,[],[f18149]) ).
fof(f33597,plain,
( spl22_1176
| ~ spl22_76
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f2985,f2959,f684,f33595]) ).
fof(f33595,plain,
( spl22_1176
<=> ! [X10,X11,X12,X9] :
( ~ in(X9,X10)
| ~ in(X9,X11)
| apply(relation_dom_restriction(X12,set_intersection2(X10,X11)),X9) = apply(X12,X9)
| ~ function(X12)
| ~ relation(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1176])]) ).
fof(f2959,plain,
( spl22_278
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_278])]) ).
fof(f2985,plain,
( ! [X10,X11,X9,X12] :
( ~ in(X9,X10)
| ~ in(X9,X11)
| apply(relation_dom_restriction(X12,set_intersection2(X10,X11)),X9) = apply(X12,X9)
| ~ function(X12)
| ~ relation(X12) )
| ~ spl22_76
| ~ spl22_278 ),
inference(resolution,[],[f2960,f685]) ).
fof(f2960,plain,
( ! [X2,X0,X1] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) )
| ~ spl22_278 ),
inference(avatar_component_clause,[],[f2959]) ).
fof(f33165,plain,
( spl22_1175
| spl22_47
| ~ spl22_934 ),
inference(avatar_split_clause,[],[f18232,f18149,f475,f33162]) ).
fof(f33162,plain,
( spl22_1175
<=> apply(relation_dom_restriction(sK19,sK3),sK10(sK3)) = apply(sK19,sK10(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1175])]) ).
fof(f18232,plain,
( apply(relation_dom_restriction(sK19,sK3),sK10(sK3)) = apply(sK19,sK10(sK3))
| spl22_47
| ~ spl22_934 ),
inference(resolution,[],[f18150,f477]) ).
fof(f32251,plain,
( ~ spl22_2
| ~ spl22_1
| spl22_1174
| ~ spl22_297
| ~ spl22_1116 ),
inference(avatar_split_clause,[],[f29141,f28754,f3075,f32248,f219,f224]) ).
fof(f32248,plain,
( spl22_1174
<=> one_to_one(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1174])]) ).
fof(f3075,plain,
( spl22_297
<=> ! [X0,X1] :
( ~ empty(relation_dom_restriction(X0,X1))
| one_to_one(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_297])]) ).
fof(f28754,plain,
( spl22_1116
<=> empty(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1116])]) ).
fof(f29141,plain,
( one_to_one(relation_dom_restriction(sK5,sK15))
| ~ relation(sK5)
| ~ function(sK5)
| ~ spl22_297
| ~ spl22_1116 ),
inference(resolution,[],[f28756,f3076]) ).
fof(f3076,plain,
( ! [X0,X1] :
( ~ empty(relation_dom_restriction(X0,X1))
| one_to_one(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_297 ),
inference(avatar_component_clause,[],[f3075]) ).
fof(f28756,plain,
( empty(relation_dom_restriction(sK5,sK15))
| ~ spl22_1116 ),
inference(avatar_component_clause,[],[f28754]) ).
fof(f31331,plain,
( spl22_1173
| ~ spl22_54
| ~ spl22_1116 ),
inference(avatar_split_clause,[],[f29144,f28754,f506,f31329]) ).
fof(f31329,plain,
( spl22_1173
<=> ! [X0] :
( relation_dom_restriction(sK5,sK15) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1173])]) ).
fof(f506,plain,
( spl22_54
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_54])]) ).
fof(f29144,plain,
( ! [X0] :
( relation_dom_restriction(sK5,sK15) = X0
| ~ empty(X0) )
| ~ spl22_54
| ~ spl22_1116 ),
inference(resolution,[],[f28756,f507]) ).
fof(f507,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl22_54 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f29896,plain,
( spl22_1172
| ~ spl22_114
| ~ spl22_1116 ),
inference(avatar_split_clause,[],[f29145,f28754,f952,f29893]) ).
fof(f29893,plain,
( spl22_1172
<=> sK15 = relation_dom_restriction(sK5,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1172])]) ).
fof(f952,plain,
( spl22_114
<=> ! [X7] :
( sK15 = X7
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_114])]) ).
fof(f29145,plain,
( sK15 = relation_dom_restriction(sK5,sK15)
| ~ spl22_114
| ~ spl22_1116 ),
inference(resolution,[],[f28756,f953]) ).
fof(f953,plain,
( ! [X7] :
( ~ empty(X7)
| sK15 = X7 )
| ~ spl22_114 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f29531,plain,
( spl22_1171
| ~ spl22_124
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4457,f4164,f1103,f29529]) ).
fof(f29529,plain,
( spl22_1171
<=> ! [X25,X27,X26] :
( sP2(powerset(X25),X26,X27)
| ~ empty(X25)
| in(sK13(powerset(X25),X26,X27),X27)
| empty(sK13(powerset(X25),X26,X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1171])]) ).
fof(f4457,plain,
( ! [X26,X27,X25] :
( sP2(powerset(X25),X26,X27)
| ~ empty(X25)
| in(sK13(powerset(X25),X26,X27),X27)
| empty(sK13(powerset(X25),X26,X27)) )
| ~ spl22_124
| ~ spl22_373 ),
inference(resolution,[],[f4165,f1104]) ).
fof(f29527,plain,
( spl22_1170
| ~ spl22_124
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4406,f4156,f1103,f29525]) ).
fof(f29525,plain,
( spl22_1170
<=> ! [X25,X27,X26] :
( sP2(X25,X26,powerset(X27))
| ~ empty(X27)
| in(sK13(X25,X26,powerset(X27)),X25)
| empty(sK13(X25,X26,powerset(X27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1170])]) ).
fof(f4406,plain,
( ! [X26,X27,X25] :
( sP2(X25,X26,powerset(X27))
| ~ empty(X27)
| in(sK13(X25,X26,powerset(X27)),X25)
| empty(sK13(X25,X26,powerset(X27))) )
| ~ spl22_124
| ~ spl22_371 ),
inference(resolution,[],[f4157,f1104]) ).
fof(f29523,plain,
( spl22_1169
| ~ spl22_124
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4355,f4148,f1103,f29521]) ).
fof(f29521,plain,
( spl22_1169
<=> ! [X25,X27,X26] :
( sP2(X25,powerset(X26),X27)
| ~ empty(X26)
| in(sK13(X25,powerset(X26),X27),X27)
| empty(sK13(X25,powerset(X26),X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1169])]) ).
fof(f4355,plain,
( ! [X26,X27,X25] :
( sP2(X25,powerset(X26),X27)
| ~ empty(X26)
| in(sK13(X25,powerset(X26),X27),X27)
| empty(sK13(X25,powerset(X26),X27)) )
| ~ spl22_124
| ~ spl22_369 ),
inference(resolution,[],[f4149,f1104]) ).
fof(f29519,plain,
( spl22_1168
| ~ spl22_124
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4304,f4139,f1103,f29517]) ).
fof(f29517,plain,
( spl22_1168
<=> ! [X25,X27,X26] :
( sP2(X25,X26,powerset(X27))
| ~ empty(X27)
| in(sK13(X25,X26,powerset(X27)),X26)
| empty(sK13(X25,X26,powerset(X27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1168])]) ).
fof(f4304,plain,
( ! [X26,X27,X25] :
( sP2(X25,X26,powerset(X27))
| ~ empty(X27)
| in(sK13(X25,X26,powerset(X27)),X26)
| empty(sK13(X25,X26,powerset(X27))) )
| ~ spl22_124
| ~ spl22_367 ),
inference(resolution,[],[f4140,f1104]) ).
fof(f29515,plain,
( spl22_1167
| ~ spl22_45
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4060,f4027,f448,f29513]) ).
fof(f29513,plain,
( spl22_1167
<=> ! [X16,X15] :
( element(sK7(X15,sK10(powerset(X16))),X16)
| sP0(X15,sK10(powerset(X16)))
| ~ in(relation_dom(X15),sK8(X15,sK10(powerset(X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1167])]) ).
fof(f4060,plain,
( ! [X16,X15] :
( element(sK7(X15,sK10(powerset(X16))),X16)
| sP0(X15,sK10(powerset(X16)))
| ~ in(relation_dom(X15),sK8(X15,sK10(powerset(X16)))) )
| ~ spl22_45
| ~ spl22_357 ),
inference(resolution,[],[f4028,f449]) ).
fof(f29511,plain,
( spl22_1166
| ~ spl22_255
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3927,f3857,f2711,f29509]) ).
fof(f29509,plain,
( spl22_1166
<=> ! [X114,X112,X113] :
( sP0(X112,powerset(X113))
| ~ empty(X113)
| in(sK8(X112,powerset(X113)),relation_dom(X112))
| sP2(sK15,X114,sK7(X112,powerset(X113))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1166])]) ).
fof(f3927,plain,
( ! [X113,X114,X112] :
( sP0(X112,powerset(X113))
| ~ empty(X113)
| in(sK8(X112,powerset(X113)),relation_dom(X112))
| sP2(sK15,X114,sK7(X112,powerset(X113))) )
| ~ spl22_255
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2712]) ).
fof(f29506,plain,
( spl22_1165
| ~ spl22_28
| ~ spl22_1116 ),
inference(avatar_split_clause,[],[f29142,f28754,f351,f29503]) ).
fof(f29503,plain,
( spl22_1165
<=> function(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1165])]) ).
fof(f351,plain,
( spl22_28
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_28])]) ).
fof(f29142,plain,
( function(relation_dom_restriction(sK5,sK15))
| ~ spl22_28
| ~ spl22_1116 ),
inference(resolution,[],[f28756,f352]) ).
fof(f352,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl22_28 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f29501,plain,
( spl22_1164
| ~ spl22_254
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3925,f3857,f2707,f29499]) ).
fof(f29499,plain,
( spl22_1164
<=> ! [X105,X107,X106] :
( sP0(X105,powerset(X106))
| ~ empty(X106)
| in(sK8(X105,powerset(X106)),relation_dom(X105))
| sP2(X107,sK15,sK7(X105,powerset(X106))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1164])]) ).
fof(f3925,plain,
( ! [X106,X107,X105] :
( sP0(X105,powerset(X106))
| ~ empty(X106)
| in(sK8(X105,powerset(X106)),relation_dom(X105))
| sP2(X107,sK15,sK7(X105,powerset(X106))) )
| ~ spl22_254
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2708]) ).
fof(f29497,plain,
( spl22_1163
| ~ spl22_253
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3924,f3857,f2703,f29495]) ).
fof(f29495,plain,
( spl22_1163
<=> ! [X102,X104,X103] :
( sP0(X102,powerset(X103))
| ~ empty(X103)
| in(sK8(X102,powerset(X103)),relation_dom(X102))
| sP2(X104,sK7(X102,powerset(X103)),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1163])]) ).
fof(f3924,plain,
( ! [X104,X102,X103] :
( sP0(X102,powerset(X103))
| ~ empty(X103)
| in(sK8(X102,powerset(X103)),relation_dom(X102))
| sP2(X104,sK7(X102,powerset(X103)),sK15) )
| ~ spl22_253
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2704]) ).
fof(f29493,plain,
( spl22_1162
| ~ spl22_252
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3923,f3857,f2699,f29491]) ).
fof(f29491,plain,
( spl22_1162
<=> ! [X100,X101,X99] :
( sP0(X99,powerset(X100))
| ~ empty(X100)
| in(sK8(X99,powerset(X100)),relation_dom(X99))
| sP2(sK7(X99,powerset(X100)),X101,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1162])]) ).
fof(f3923,plain,
( ! [X101,X99,X100] :
( sP0(X99,powerset(X100))
| ~ empty(X100)
| in(sK8(X99,powerset(X100)),relation_dom(X99))
| sP2(sK7(X99,powerset(X100)),X101,sK15) )
| ~ spl22_252
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2700]) ).
fof(f29489,plain,
( spl22_1161
| ~ spl22_56
| ~ spl22_347 ),
inference(avatar_split_clause,[],[f3841,f3831,f540,f29487]) ).
fof(f29487,plain,
( spl22_1161
<=> ! [X9,X8] :
( sP2(sK10(powerset(X8)),X9,sK10(powerset(X8)))
| empty(X8)
| in(sK13(sK10(powerset(X8)),X9,sK10(powerset(X8))),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1161])]) ).
fof(f3841,plain,
( ! [X8,X9] :
( sP2(sK10(powerset(X8)),X9,sK10(powerset(X8)))
| empty(X8)
| in(sK13(sK10(powerset(X8)),X9,sK10(powerset(X8))),X8) )
| ~ spl22_56
| ~ spl22_347 ),
inference(resolution,[],[f3832,f541]) ).
fof(f29485,plain,
( spl22_1160
| ~ spl22_56
| ~ spl22_346 ),
inference(avatar_split_clause,[],[f3837,f3827,f540,f29483]) ).
fof(f29483,plain,
( spl22_1160
<=> ! [X9,X8] :
( sP2(X8,sK10(powerset(X9)),sK10(powerset(X9)))
| empty(X9)
| in(sK13(X8,sK10(powerset(X9)),sK10(powerset(X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1160])]) ).
fof(f3837,plain,
( ! [X8,X9] :
( sP2(X8,sK10(powerset(X9)),sK10(powerset(X9)))
| empty(X9)
| in(sK13(X8,sK10(powerset(X9)),sK10(powerset(X9))),X9) )
| ~ spl22_56
| ~ spl22_346 ),
inference(resolution,[],[f3828,f541]) ).
fof(f29481,plain,
( spl22_1159
| ~ spl22_37
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3787,f3750,f397,f29479]) ).
fof(f29479,plain,
( spl22_1159
<=> ! [X6,X5] :
( apply(relation_dom_restriction(relation_dom(X5),powerset(X6)),sK15) = apply(relation_dom(X5),sK15)
| ~ function(relation_dom(X5))
| empty(powerset(X6))
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1159])]) ).
fof(f3787,plain,
( ! [X6,X5] :
( apply(relation_dom_restriction(relation_dom(X5),powerset(X6)),sK15) = apply(relation_dom(X5),sK15)
| ~ function(relation_dom(X5))
| empty(powerset(X6))
| ~ empty(X5) )
| ~ spl22_37
| ~ spl22_342 ),
inference(resolution,[],[f3751,f398]) ).
fof(f29477,plain,
( spl22_1158
| ~ spl22_35
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3786,f3750,f389,f29475]) ).
fof(f29475,plain,
( spl22_1158
<=> ! [X4,X3] :
( apply(relation_dom_restriction(relation_rng(X3),powerset(X4)),sK15) = apply(relation_rng(X3),sK15)
| ~ function(relation_rng(X3))
| empty(powerset(X4))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1158])]) ).
fof(f3786,plain,
( ! [X3,X4] :
( apply(relation_dom_restriction(relation_rng(X3),powerset(X4)),sK15) = apply(relation_rng(X3),sK15)
| ~ function(relation_rng(X3))
| empty(powerset(X4))
| ~ empty(X3) )
| ~ spl22_35
| ~ spl22_342 ),
inference(resolution,[],[f3751,f390]) ).
fof(f29473,plain,
( spl22_1157
| ~ spl22_37
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3768,f3746,f397,f29471]) ).
fof(f29471,plain,
( spl22_1157
<=> ! [X6,X5] :
( apply(relation_dom_restriction(relation_dom(X5),X6),sK10(X6)) = apply(relation_dom(X5),sK10(X6))
| ~ function(relation_dom(X5))
| empty(X6)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1157])]) ).
fof(f3768,plain,
( ! [X6,X5] :
( apply(relation_dom_restriction(relation_dom(X5),X6),sK10(X6)) = apply(relation_dom(X5),sK10(X6))
| ~ function(relation_dom(X5))
| empty(X6)
| ~ empty(X5) )
| ~ spl22_37
| ~ spl22_341 ),
inference(resolution,[],[f3747,f398]) ).
fof(f29469,plain,
( spl22_1156
| ~ spl22_35
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3767,f3746,f389,f29467]) ).
fof(f29467,plain,
( spl22_1156
<=> ! [X4,X3] :
( apply(relation_dom_restriction(relation_rng(X3),X4),sK10(X4)) = apply(relation_rng(X3),sK10(X4))
| ~ function(relation_rng(X3))
| empty(X4)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1156])]) ).
fof(f3767,plain,
( ! [X3,X4] :
( apply(relation_dom_restriction(relation_rng(X3),X4),sK10(X4)) = apply(relation_rng(X3),sK10(X4))
| ~ function(relation_rng(X3))
| empty(X4)
| ~ empty(X3) )
| ~ spl22_35
| ~ spl22_341 ),
inference(resolution,[],[f3747,f390]) ).
fof(f29465,plain,
( spl22_1155
| ~ spl22_65
| ~ spl22_337 ),
inference(avatar_split_clause,[],[f3735,f3449,f610,f29463]) ).
fof(f29463,plain,
( spl22_1155
<=> ! [X2,X0,X1,X3] :
( sP2(powerset(X0),X1,sK10(powerset(X2)))
| ~ empty(X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,sK10(powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1155])]) ).
fof(f3735,plain,
( ! [X2,X3,X0,X1] :
( sP2(powerset(X0),X1,sK10(powerset(X2)))
| ~ empty(X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,sK10(powerset(X2)))) )
| ~ spl22_65
| ~ spl22_337 ),
inference(resolution,[],[f3450,f611]) ).
fof(f29368,plain,
( spl22_1154
| ~ spl22_65
| ~ spl22_335 ),
inference(avatar_split_clause,[],[f3730,f3441,f610,f29366]) ).
fof(f29366,plain,
( spl22_1154
<=> ! [X2,X0,X1,X3] :
( sP2(sK10(powerset(X0)),X1,powerset(X2))
| ~ empty(X0)
| ~ empty(X2)
| ~ in(X3,sK13(sK10(powerset(X0)),X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1154])]) ).
fof(f3730,plain,
( ! [X2,X3,X0,X1] :
( sP2(sK10(powerset(X0)),X1,powerset(X2))
| ~ empty(X0)
| ~ empty(X2)
| ~ in(X3,sK13(sK10(powerset(X0)),X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_335 ),
inference(resolution,[],[f3442,f611]) ).
fof(f29364,plain,
( spl22_1153
| ~ spl22_65
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f3712,f3429,f610,f29362]) ).
fof(f29362,plain,
( spl22_1153
<=> ! [X2,X0,X1,X3] :
( sP2(X0,powerset(X1),sK10(powerset(X2)))
| ~ empty(X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),sK10(powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1153])]) ).
fof(f3712,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,powerset(X1),sK10(powerset(X2)))
| ~ empty(X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),sK10(powerset(X2)))) )
| ~ spl22_65
| ~ spl22_332 ),
inference(resolution,[],[f3430,f611]) ).
fof(f29360,plain,
( spl22_1152
| ~ spl22_65
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f3707,f3421,f610,f29358]) ).
fof(f29358,plain,
( spl22_1152
<=> ! [X2,X0,X1,X3] :
( sP2(X0,sK10(powerset(X1)),powerset(X2))
| ~ empty(X1)
| ~ empty(X2)
| ~ in(X3,sK13(X0,sK10(powerset(X1)),powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1152])]) ).
fof(f3707,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,sK10(powerset(X1)),powerset(X2))
| ~ empty(X1)
| ~ empty(X2)
| ~ in(X3,sK13(X0,sK10(powerset(X1)),powerset(X2))) )
| ~ spl22_65
| ~ spl22_330 ),
inference(resolution,[],[f3422,f611]) ).
fof(f29356,plain,
( spl22_1151
| ~ spl22_65
| ~ spl22_327 ),
inference(avatar_split_clause,[],[f3693,f3392,f610,f29354]) ).
fof(f29354,plain,
( spl22_1151
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X0,X1,sK10(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1151])]) ).
fof(f3693,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,sK10(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,sK10(powerset(powerset(X2))))) )
| ~ spl22_65
| ~ spl22_327 ),
inference(resolution,[],[f3393,f611]) ).
fof(f29352,plain,
( spl22_1150
| ~ spl22_65
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3684,f3384,f610,f29350]) ).
fof(f29350,plain,
( spl22_1150
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(sK10(powerset(powerset(X1))),X2,X0)
| ~ empty(X1)
| ~ in(X3,sK13(sK10(powerset(powerset(X1))),X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1150])]) ).
fof(f3684,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(sK10(powerset(powerset(X1))),X2,X0)
| ~ empty(X1)
| ~ in(X3,sK13(sK10(powerset(powerset(X1))),X2,X0)) )
| ~ spl22_65
| ~ spl22_325 ),
inference(resolution,[],[f3385,f611]) ).
fof(f29348,plain,
( spl22_1149
| ~ spl22_65
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3675,f3376,f610,f29346]) ).
fof(f29346,plain,
( spl22_1149
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,X0,sK10(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1149])]) ).
fof(f3675,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,sK10(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,sK10(powerset(powerset(X2))))) )
| ~ spl22_65
| ~ spl22_323 ),
inference(resolution,[],[f3377,f611]) ).
fof(f29344,plain,
( spl22_1148
| ~ spl22_65
| ~ spl22_321 ),
inference(avatar_split_clause,[],[f3658,f3368,f610,f29342]) ).
fof(f29342,plain,
( spl22_1148
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(powerset(X2))),X0)
| ~ empty(X2)
| ~ in(X3,sK13(X1,sK10(powerset(powerset(X2))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1148])]) ).
fof(f3658,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK10(powerset(powerset(X2))),X0)
| ~ empty(X2)
| ~ in(X3,sK13(X1,sK10(powerset(powerset(X2))),X0)) )
| ~ spl22_65
| ~ spl22_321 ),
inference(resolution,[],[f3369,f611]) ).
fof(f29340,plain,
( spl22_1147
| ~ spl22_137
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3537,f3327,f1213,f29338]) ).
fof(f29338,plain,
( spl22_1147
<=> ! [X45,X46,X47] :
( ~ empty(X45)
| sP2(sK10(powerset(X45)),X46,sK10(powerset(X47)))
| element(sK13(sK10(powerset(X45)),X46,sK10(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1147])]) ).
fof(f3537,plain,
( ! [X46,X47,X45] :
( ~ empty(X45)
| sP2(sK10(powerset(X45)),X46,sK10(powerset(X47)))
| element(sK13(sK10(powerset(X45)),X46,sK10(powerset(X47))),X47) )
| ~ spl22_137
| ~ spl22_315 ),
inference(resolution,[],[f3328,f1214]) ).
fof(f29336,plain,
( spl22_1146
| ~ spl22_141
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3536,f3327,f1277,f29334]) ).
fof(f29334,plain,
( spl22_1146
<=> ! [X44,X43,X42] :
( ~ empty(X42)
| sP2(sK10(powerset(X42)),X43,sK6(X44))
| element(sK13(sK10(powerset(X42)),X43,sK6(X44)),X44)
| empty(X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1146])]) ).
fof(f3536,plain,
( ! [X44,X42,X43] :
( ~ empty(X42)
| sP2(sK10(powerset(X42)),X43,sK6(X44))
| element(sK13(sK10(powerset(X42)),X43,sK6(X44)),X44)
| empty(X44) )
| ~ spl22_141
| ~ spl22_315 ),
inference(resolution,[],[f3328,f1278]) ).
fof(f29332,plain,
( spl22_1145
| ~ spl22_237
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3530,f3327,f2435,f29330]) ).
fof(f29330,plain,
( spl22_1145
<=> ! [X20,X21,X23,X22] :
( ~ empty(X20)
| sP2(sK10(powerset(X20)),X21,set_intersection2(X22,X23))
| in(sK13(sK10(powerset(X20)),X21,set_intersection2(X22,X23)),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1145])]) ).
fof(f3530,plain,
( ! [X21,X22,X23,X20] :
( ~ empty(X20)
| sP2(sK10(powerset(X20)),X21,set_intersection2(X22,X23))
| in(sK13(sK10(powerset(X20)),X21,set_intersection2(X22,X23)),X23) )
| ~ spl22_237
| ~ spl22_315 ),
inference(resolution,[],[f3328,f2436]) ).
fof(f29138,plain,
( spl22_1144
| ~ spl22_238
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3529,f3327,f2439,f29136]) ).
fof(f29136,plain,
( spl22_1144
<=> ! [X18,X17,X16,X19] :
( ~ empty(X16)
| sP2(sK10(powerset(X16)),X17,set_intersection2(X18,X19))
| in(sK13(sK10(powerset(X16)),X17,set_intersection2(X18,X19)),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1144])]) ).
fof(f3529,plain,
( ! [X18,X19,X16,X17] :
( ~ empty(X16)
| sP2(sK10(powerset(X16)),X17,set_intersection2(X18,X19))
| in(sK13(sK10(powerset(X16)),X17,set_intersection2(X18,X19)),X18) )
| ~ spl22_238
| ~ spl22_315 ),
inference(resolution,[],[f3328,f2440]) ).
fof(f29134,plain,
( spl22_1143
| ~ spl22_137
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3520,f3323,f1213,f29132]) ).
fof(f29132,plain,
( spl22_1143
<=> ! [X45,X46,X47] :
( ~ empty(X45)
| sP2(X46,sK10(powerset(X45)),sK10(powerset(X47)))
| element(sK13(X46,sK10(powerset(X45)),sK10(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1143])]) ).
fof(f3520,plain,
( ! [X46,X47,X45] :
( ~ empty(X45)
| sP2(X46,sK10(powerset(X45)),sK10(powerset(X47)))
| element(sK13(X46,sK10(powerset(X45)),sK10(powerset(X47))),X47) )
| ~ spl22_137
| ~ spl22_314 ),
inference(resolution,[],[f3324,f1214]) ).
fof(f29130,plain,
( spl22_1142
| ~ spl22_141
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3519,f3323,f1277,f29128]) ).
fof(f29128,plain,
( spl22_1142
<=> ! [X44,X43,X42] :
( ~ empty(X42)
| sP2(X43,sK10(powerset(X42)),sK6(X44))
| element(sK13(X43,sK10(powerset(X42)),sK6(X44)),X44)
| empty(X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1142])]) ).
fof(f3519,plain,
( ! [X44,X42,X43] :
( ~ empty(X42)
| sP2(X43,sK10(powerset(X42)),sK6(X44))
| element(sK13(X43,sK10(powerset(X42)),sK6(X44)),X44)
| empty(X44) )
| ~ spl22_141
| ~ spl22_314 ),
inference(resolution,[],[f3324,f1278]) ).
fof(f29126,plain,
( spl22_1141
| ~ spl22_237
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3513,f3323,f2435,f29124]) ).
fof(f29124,plain,
( spl22_1141
<=> ! [X20,X21,X23,X22] :
( ~ empty(X20)
| sP2(X21,sK10(powerset(X20)),set_intersection2(X22,X23))
| in(sK13(X21,sK10(powerset(X20)),set_intersection2(X22,X23)),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1141])]) ).
fof(f3513,plain,
( ! [X21,X22,X23,X20] :
( ~ empty(X20)
| sP2(X21,sK10(powerset(X20)),set_intersection2(X22,X23))
| in(sK13(X21,sK10(powerset(X20)),set_intersection2(X22,X23)),X23) )
| ~ spl22_237
| ~ spl22_314 ),
inference(resolution,[],[f3324,f2436]) ).
fof(f29122,plain,
( spl22_1140
| ~ spl22_238
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3512,f3323,f2439,f29120]) ).
fof(f29120,plain,
( spl22_1140
<=> ! [X18,X17,X16,X19] :
( ~ empty(X16)
| sP2(X17,sK10(powerset(X16)),set_intersection2(X18,X19))
| in(sK13(X17,sK10(powerset(X16)),set_intersection2(X18,X19)),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1140])]) ).
fof(f3512,plain,
( ! [X18,X19,X16,X17] :
( ~ empty(X16)
| sP2(X17,sK10(powerset(X16)),set_intersection2(X18,X19))
| in(sK13(X17,sK10(powerset(X16)),set_intersection2(X18,X19)),X18) )
| ~ spl22_238
| ~ spl22_314 ),
inference(resolution,[],[f3324,f2440]) ).
fof(f29118,plain,
( spl22_1139
| ~ spl22_137
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3503,f3319,f1213,f29116]) ).
fof(f29116,plain,
( spl22_1139
<=> ! [X45,X44,X46] :
( ~ empty(X44)
| sP2(X45,sK10(powerset(X46)),sK10(powerset(X44)))
| element(sK13(X45,sK10(powerset(X46)),sK10(powerset(X44))),X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1139])]) ).
fof(f3503,plain,
( ! [X46,X44,X45] :
( ~ empty(X44)
| sP2(X45,sK10(powerset(X46)),sK10(powerset(X44)))
| element(sK13(X45,sK10(powerset(X46)),sK10(powerset(X44))),X46) )
| ~ spl22_137
| ~ spl22_313 ),
inference(resolution,[],[f3320,f1214]) ).
fof(f29114,plain,
( spl22_1138
| ~ spl22_141
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3502,f3319,f1277,f29112]) ).
fof(f29112,plain,
( spl22_1138
<=> ! [X41,X43,X42] :
( ~ empty(X41)
| sP2(X42,sK6(X43),sK10(powerset(X41)))
| element(sK13(X42,sK6(X43),sK10(powerset(X41))),X43)
| empty(X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1138])]) ).
fof(f3502,plain,
( ! [X41,X42,X43] :
( ~ empty(X41)
| sP2(X42,sK6(X43),sK10(powerset(X41)))
| element(sK13(X42,sK6(X43),sK10(powerset(X41))),X43)
| empty(X43) )
| ~ spl22_141
| ~ spl22_313 ),
inference(resolution,[],[f3320,f1278]) ).
fof(f29110,plain,
( spl22_1137
| ~ spl22_237
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3496,f3319,f2435,f29108]) ).
fof(f29108,plain,
( spl22_1137
<=> ! [X19,X20,X21,X22] :
( ~ empty(X19)
| sP2(X20,set_intersection2(X21,X22),sK10(powerset(X19)))
| in(sK13(X20,set_intersection2(X21,X22),sK10(powerset(X19))),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1137])]) ).
fof(f3496,plain,
( ! [X21,X19,X22,X20] :
( ~ empty(X19)
| sP2(X20,set_intersection2(X21,X22),sK10(powerset(X19)))
| in(sK13(X20,set_intersection2(X21,X22),sK10(powerset(X19))),X22) )
| ~ spl22_237
| ~ spl22_313 ),
inference(resolution,[],[f3320,f2436]) ).
fof(f29106,plain,
( spl22_1136
| ~ spl22_238
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3495,f3319,f2439,f29104]) ).
fof(f29104,plain,
( spl22_1136
<=> ! [X18,X17,X16,X15] :
( ~ empty(X15)
| sP2(X16,set_intersection2(X17,X18),sK10(powerset(X15)))
| in(sK13(X16,set_intersection2(X17,X18),sK10(powerset(X15))),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1136])]) ).
fof(f3495,plain,
( ! [X18,X16,X17,X15] :
( ~ empty(X15)
| sP2(X16,set_intersection2(X17,X18),sK10(powerset(X15)))
| in(sK13(X16,set_intersection2(X17,X18),sK10(powerset(X15))),X17) )
| ~ spl22_238
| ~ spl22_313 ),
inference(resolution,[],[f3320,f2440]) ).
fof(f29102,plain,
( spl22_1135
| ~ spl22_137
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3469,f3315,f1213,f29100]) ).
fof(f29100,plain,
( spl22_1135
<=> ! [X45,X44,X46] :
( ~ empty(X44)
| sP2(sK10(powerset(X45)),X46,sK10(powerset(X44)))
| element(sK13(sK10(powerset(X45)),X46,sK10(powerset(X44))),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1135])]) ).
fof(f3469,plain,
( ! [X46,X44,X45] :
( ~ empty(X44)
| sP2(sK10(powerset(X45)),X46,sK10(powerset(X44)))
| element(sK13(sK10(powerset(X45)),X46,sK10(powerset(X44))),X45) )
| ~ spl22_137
| ~ spl22_312 ),
inference(resolution,[],[f3316,f1214]) ).
fof(f29098,plain,
( ~ spl22_1
| ~ spl22_44
| spl22_1117 ),
inference(avatar_split_clause,[],[f29057,f28758,f444,f219]) ).
fof(f28758,plain,
( spl22_1117
<=> relation(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1117])]) ).
fof(f29057,plain,
( ~ relation(sK5)
| ~ spl22_44
| spl22_1117 ),
inference(resolution,[],[f28760,f445]) ).
fof(f28760,plain,
( ~ relation(relation_dom_restriction(sK5,sK15))
| spl22_1117 ),
inference(avatar_component_clause,[],[f28758]) ).
fof(f29097,plain,
( spl22_1134
| ~ spl22_141
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3468,f3315,f1277,f29095]) ).
fof(f29095,plain,
( spl22_1134
<=> ! [X41,X43,X42] :
( ~ empty(X41)
| sP2(sK6(X42),X43,sK10(powerset(X41)))
| element(sK13(sK6(X42),X43,sK10(powerset(X41))),X42)
| empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1134])]) ).
fof(f3468,plain,
( ! [X41,X42,X43] :
( ~ empty(X41)
| sP2(sK6(X42),X43,sK10(powerset(X41)))
| element(sK13(sK6(X42),X43,sK10(powerset(X41))),X42)
| empty(X42) )
| ~ spl22_141
| ~ spl22_312 ),
inference(resolution,[],[f3316,f1278]) ).
fof(f29093,plain,
( spl22_1133
| ~ spl22_237
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3462,f3315,f2435,f29091]) ).
fof(f29091,plain,
( spl22_1133
<=> ! [X19,X20,X21,X22] :
( ~ empty(X19)
| sP2(set_intersection2(X20,X21),X22,sK10(powerset(X19)))
| in(sK13(set_intersection2(X20,X21),X22,sK10(powerset(X19))),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1133])]) ).
fof(f3462,plain,
( ! [X21,X19,X22,X20] :
( ~ empty(X19)
| sP2(set_intersection2(X20,X21),X22,sK10(powerset(X19)))
| in(sK13(set_intersection2(X20,X21),X22,sK10(powerset(X19))),X21) )
| ~ spl22_237
| ~ spl22_312 ),
inference(resolution,[],[f3316,f2436]) ).
fof(f29089,plain,
( spl22_1132
| ~ spl22_238
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3461,f3315,f2439,f29087]) ).
fof(f29087,plain,
( spl22_1132
<=> ! [X18,X17,X16,X15] :
( ~ empty(X15)
| sP2(set_intersection2(X16,X17),X18,sK10(powerset(X15)))
| in(sK13(set_intersection2(X16,X17),X18,sK10(powerset(X15))),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1132])]) ).
fof(f3461,plain,
( ! [X18,X16,X17,X15] :
( ~ empty(X15)
| sP2(set_intersection2(X16,X17),X18,sK10(powerset(X15)))
| in(sK13(set_intersection2(X16,X17),X18,sK10(powerset(X15))),X16) )
| ~ spl22_238
| ~ spl22_312 ),
inference(resolution,[],[f3316,f2440]) ).
fof(f29085,plain,
( spl22_1131
| ~ spl22_67
| ~ spl22_309 ),
inference(avatar_split_clause,[],[f3297,f3268,f633,f29083]) ).
fof(f29083,plain,
( spl22_1131
<=> ! [X5,X4,X7,X6] :
( ~ sP0(X4,sK6(powerset(X5)))
| ~ in(X6,relation_dom(X4))
| empty(powerset(X5))
| element(X7,X5)
| ~ in(X7,apply(X4,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1131])]) ).
fof(f3268,plain,
( spl22_309
<=> ! [X13,X14,X15] :
( ~ in(X13,relation_dom(X14))
| ~ sP0(X14,sK6(X15))
| element(apply(X14,X13),X15)
| empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_309])]) ).
fof(f3297,plain,
( ! [X6,X7,X4,X5] :
( ~ sP0(X4,sK6(powerset(X5)))
| ~ in(X6,relation_dom(X4))
| empty(powerset(X5))
| element(X7,X5)
| ~ in(X7,apply(X4,X6)) )
| ~ spl22_67
| ~ spl22_309 ),
inference(resolution,[],[f3269,f634]) ).
fof(f3269,plain,
( ! [X14,X15,X13] :
( element(apply(X14,X13),X15)
| ~ sP0(X14,sK6(X15))
| ~ in(X13,relation_dom(X14))
| empty(X15) )
| ~ spl22_309 ),
inference(avatar_component_clause,[],[f3268]) ).
fof(f29081,plain,
( spl22_1130
| ~ spl22_67
| ~ spl22_308 ),
inference(avatar_split_clause,[],[f3289,f3264,f633,f29079]) ).
fof(f29079,plain,
( spl22_1130
<=> ! [X4,X5,X3] :
( ~ empty(relation_dom(X3))
| sP0(X3,sK10(powerset(powerset(X4))))
| element(X5,X4)
| ~ in(X5,sK7(X3,sK10(powerset(powerset(X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1130])]) ).
fof(f3264,plain,
( spl22_308
<=> ! [X11,X12] :
( sP0(X11,sK10(powerset(X12)))
| ~ empty(relation_dom(X11))
| element(sK7(X11,sK10(powerset(X12))),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_308])]) ).
fof(f3289,plain,
( ! [X3,X4,X5] :
( ~ empty(relation_dom(X3))
| sP0(X3,sK10(powerset(powerset(X4))))
| element(X5,X4)
| ~ in(X5,sK7(X3,sK10(powerset(powerset(X4))))) )
| ~ spl22_67
| ~ spl22_308 ),
inference(resolution,[],[f3265,f634]) ).
fof(f3265,plain,
( ! [X11,X12] :
( element(sK7(X11,sK10(powerset(X12))),X12)
| ~ empty(relation_dom(X11))
| sP0(X11,sK10(powerset(X12))) )
| ~ spl22_308 ),
inference(avatar_component_clause,[],[f3264]) ).
fof(f29077,plain,
( spl22_1129
| ~ spl22_65
| ~ spl22_307 ),
inference(avatar_split_clause,[],[f3283,f3260,f610,f29075]) ).
fof(f29075,plain,
( spl22_1129
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK6(powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK6(powerset(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1129])]) ).
fof(f3283,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK6(powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK6(powerset(X1)))) )
| ~ spl22_65
| ~ spl22_307 ),
inference(resolution,[],[f3261,f611]) ).
fof(f29073,plain,
( spl22_1128
| ~ spl22_67
| ~ spl22_302 ),
inference(avatar_split_clause,[],[f3245,f3229,f633,f29071]) ).
fof(f29071,plain,
( spl22_1128
<=> ! [X4,X5,X3] :
( element(sK8(X3,powerset(X4)),relation_dom(X3))
| sP0(X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1128])]) ).
fof(f3229,plain,
( spl22_302
<=> ! [X6,X5] :
( element(sK8(X5,X6),relation_dom(X5))
| sP0(X5,X6)
| element(sK7(X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_302])]) ).
fof(f3245,plain,
( ! [X3,X4,X5] :
( element(sK8(X3,powerset(X4)),relation_dom(X3))
| sP0(X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) )
| ~ spl22_67
| ~ spl22_302 ),
inference(resolution,[],[f3230,f634]) ).
fof(f3230,plain,
( ! [X6,X5] :
( element(sK8(X5,X6),relation_dom(X5))
| element(sK7(X5,X6),X6)
| sP0(X5,X6) )
| ~ spl22_302 ),
inference(avatar_component_clause,[],[f3229]) ).
fof(f29069,plain,
( spl22_1127
| ~ spl22_156
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3134,f3027,f1407,f29067]) ).
fof(f29067,plain,
( spl22_1127
<=> ! [X85,X83,X84,X86] :
( ~ sP0(X83,sK13(apply(X83,X84),X85,X86))
| ~ in(X84,relation_dom(X83))
| sP2(apply(X83,X84),X85,X86)
| ~ empty(X86) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1127])]) ).
fof(f3134,plain,
( ! [X83,X86,X84,X85] :
( ~ sP0(X83,sK13(apply(X83,X84),X85,X86))
| ~ in(X84,relation_dom(X83))
| sP2(apply(X83,X84),X85,X86)
| ~ empty(X86) )
| ~ spl22_156
| ~ spl22_288 ),
inference(resolution,[],[f3028,f1408]) ).
fof(f29065,plain,
( spl22_1126
| ~ spl22_154
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3130,f3027,f1399,f29063]) ).
fof(f29063,plain,
( spl22_1126
<=> ! [X69,X70,X67,X68] :
( ~ sP0(X67,sK13(X68,apply(X67,X69),X70))
| ~ in(X69,relation_dom(X67))
| sP2(X68,apply(X67,X69),X70)
| ~ empty(X70) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1126])]) ).
fof(f3130,plain,
( ! [X70,X68,X69,X67] :
( ~ sP0(X67,sK13(X68,apply(X67,X69),X70))
| ~ in(X69,relation_dom(X67))
| sP2(X68,apply(X67,X69),X70)
| ~ empty(X70) )
| ~ spl22_154
| ~ spl22_288 ),
inference(resolution,[],[f3028,f1400]) ).
fof(f29061,plain,
( spl22_1125
| ~ spl22_157
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3123,f3027,f1411,f29059]) ).
fof(f29059,plain,
( spl22_1125
<=> ! [X41,X40,X42,X39] :
( ~ sP0(X39,sK13(X40,X41,apply(X39,X42)))
| ~ in(X42,relation_dom(X39))
| sP2(X40,X41,apply(X39,X42))
| ~ empty(X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1125])]) ).
fof(f3123,plain,
( ! [X40,X41,X39,X42] :
( ~ sP0(X39,sK13(X40,X41,apply(X39,X42)))
| ~ in(X42,relation_dom(X39))
| sP2(X40,X41,apply(X39,X42))
| ~ empty(X40) )
| ~ spl22_157
| ~ spl22_288 ),
inference(resolution,[],[f3028,f1412]) ).
fof(f29056,plain,
( spl22_1124
| ~ spl22_155
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3122,f3027,f1403,f29054]) ).
fof(f29054,plain,
( spl22_1124
<=> ! [X38,X36,X35,X37] :
( ~ sP0(X35,sK13(X36,X37,apply(X35,X38)))
| ~ in(X38,relation_dom(X35))
| sP2(X36,X37,apply(X35,X38))
| ~ empty(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1124])]) ).
fof(f3122,plain,
( ! [X38,X36,X37,X35] :
( ~ sP0(X35,sK13(X36,X37,apply(X35,X38)))
| ~ in(X38,relation_dom(X35))
| sP2(X36,X37,apply(X35,X38))
| ~ empty(X37) )
| ~ spl22_155
| ~ spl22_288 ),
inference(resolution,[],[f3028,f1404]) ).
fof(f29052,plain,
( spl22_1123
| ~ spl22_59
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2935,f2799,f552,f29050]) ).
fof(f29050,plain,
( spl22_1123
<=> ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| set_intersection2(X0,X1) = relation_dom_restriction(set_intersection2(X0,X1),relation_dom(set_intersection2(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1123])]) ).
fof(f2799,plain,
( spl22_276
<=> ! [X1] :
( relation_dom_restriction(X1,relation_dom(X1)) = X1
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_276])]) ).
fof(f2935,plain,
( ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| set_intersection2(X0,X1) = relation_dom_restriction(set_intersection2(X0,X1),relation_dom(set_intersection2(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_276 ),
inference(resolution,[],[f2800,f553]) ).
fof(f2800,plain,
( ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_dom_restriction(X1,relation_dom(X1)) = X1 )
| ~ spl22_276 ),
inference(avatar_component_clause,[],[f2799]) ).
fof(f29048,plain,
( spl22_1122
| ~ spl22_79
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2672,f2571,f718,f29046]) ).
fof(f29046,plain,
( spl22_1122
<=> ! [X16,X14,X15] :
( ~ sP0(X14,X15)
| ~ empty(X15)
| sK7(X16,relation_dom(X14)) = apply(X16,sK8(X16,relation_dom(X14)))
| sP0(X16,relation_dom(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1122])]) ).
fof(f2672,plain,
( ! [X16,X14,X15] :
( ~ sP0(X14,X15)
| ~ empty(X15)
| sK7(X16,relation_dom(X14)) = apply(X16,sK8(X16,relation_dom(X14)))
| sP0(X16,relation_dom(X14)) )
| ~ spl22_79
| ~ spl22_250 ),
inference(resolution,[],[f2572,f719]) ).
fof(f29044,plain,
( spl22_1121
| ~ spl22_74
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2507,f2439,f668,f29042]) ).
fof(f29042,plain,
( spl22_1121
<=> ! [X18,X16,X17] :
( in(sK7(X16,set_intersection2(X17,X18)),X17)
| in(sK8(X16,set_intersection2(X17,X18)),relation_dom(X16))
| sP0(X16,set_intersection2(X17,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1121])]) ).
fof(f668,plain,
( spl22_74
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_74])]) ).
fof(f2507,plain,
( ! [X18,X16,X17] :
( in(sK7(X16,set_intersection2(X17,X18)),X17)
| in(sK8(X16,set_intersection2(X17,X18)),relation_dom(X16))
| sP0(X16,set_intersection2(X17,X18)) )
| ~ spl22_74
| ~ spl22_238 ),
inference(resolution,[],[f2440,f669]) ).
fof(f669,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_74 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f29040,plain,
( spl22_1120
| ~ spl22_159
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2504,f2439,f1481,f29038]) ).
fof(f29038,plain,
( spl22_1120
<=> ! [X9,X8,X7] :
( in(sK7(X7,set_intersection2(X8,X9)),X8)
| element(sK8(X7,set_intersection2(X8,X9)),relation_dom(X7))
| sP0(X7,set_intersection2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1120])]) ).
fof(f2504,plain,
( ! [X8,X9,X7] :
( in(sK7(X7,set_intersection2(X8,X9)),X8)
| element(sK8(X7,set_intersection2(X8,X9)),relation_dom(X7))
| sP0(X7,set_intersection2(X8,X9)) )
| ~ spl22_159
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1482]) ).
fof(f29036,plain,
( spl22_1119
| ~ spl22_74
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2476,f2435,f668,f29034]) ).
fof(f29034,plain,
( spl22_1119
<=> ! [X18,X16,X17] :
( in(sK7(X16,set_intersection2(X17,X18)),X18)
| in(sK8(X16,set_intersection2(X17,X18)),relation_dom(X16))
| sP0(X16,set_intersection2(X17,X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1119])]) ).
fof(f2476,plain,
( ! [X18,X16,X17] :
( in(sK7(X16,set_intersection2(X17,X18)),X18)
| in(sK8(X16,set_intersection2(X17,X18)),relation_dom(X16))
| sP0(X16,set_intersection2(X17,X18)) )
| ~ spl22_74
| ~ spl22_237 ),
inference(resolution,[],[f2436,f669]) ).
fof(f29032,plain,
( spl22_1118
| ~ spl22_159
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2473,f2435,f1481,f29030]) ).
fof(f29030,plain,
( spl22_1118
<=> ! [X9,X8,X7] :
( in(sK7(X7,set_intersection2(X8,X9)),X9)
| element(sK8(X7,set_intersection2(X8,X9)),relation_dom(X7))
| sP0(X7,set_intersection2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1118])]) ).
fof(f2473,plain,
( ! [X8,X9,X7] :
( in(sK7(X7,set_intersection2(X8,X9)),X9)
| element(sK8(X7,set_intersection2(X8,X9)),relation_dom(X7))
| sP0(X7,set_intersection2(X8,X9)) )
| ~ spl22_159
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1482]) ).
fof(f28761,plain,
( spl22_1116
| ~ spl22_1117
| ~ spl22_10
| ~ spl22_49
| ~ spl22_1089 ),
inference(avatar_split_clause,[],[f27981,f27339,f486,f264,f28758,f28754]) ).
fof(f264,plain,
( spl22_10
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).
fof(f486,plain,
( spl22_49
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_49])]) ).
fof(f27339,plain,
( spl22_1089
<=> sK15 = relation_rng(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1089])]) ).
fof(f27981,plain,
( ~ empty(sK15)
| ~ relation(relation_dom_restriction(sK5,sK15))
| empty(relation_dom_restriction(sK5,sK15))
| ~ spl22_49
| ~ spl22_1089 ),
inference(superposition,[],[f487,f27341]) ).
fof(f27341,plain,
( sK15 = relation_rng(relation_dom_restriction(sK5,sK15))
| ~ spl22_1089 ),
inference(avatar_component_clause,[],[f27339]) ).
fof(f487,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl22_49 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f27448,plain,
( spl22_1115
| ~ spl22_116
| ~ spl22_430 ),
inference(avatar_split_clause,[],[f6063,f6030,f959,f27446]) ).
fof(f27446,plain,
( spl22_1115
<=> ! [X116,X115] :
( apply(sK15,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK15,X115),sK13(X115,X116,sK15))
| sP2(X115,X116,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1115])]) ).
fof(f959,plain,
( spl22_116
<=> ! [X8] : ~ in(X8,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_116])]) ).
fof(f6063,plain,
( ! [X116,X115] :
( apply(sK15,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK15,X115),sK13(X115,X116,sK15))
| sP2(X115,X116,sK15) )
| ~ spl22_116
| ~ spl22_430 ),
inference(resolution,[],[f6031,f960]) ).
fof(f960,plain,
( ! [X8] : ~ in(X8,sK15)
| ~ spl22_116 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f27444,plain,
( spl22_1114
| ~ spl22_116
| ~ spl22_429 ),
inference(avatar_split_clause,[],[f6024,f5991,f959,f27442]) ).
fof(f27442,plain,
( spl22_1114
<=> ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK20,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK20,X115),sK13(X115,X116,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1114])]) ).
fof(f6024,plain,
( ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK20,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK20,X115),sK13(X115,X116,sK15)) )
| ~ spl22_116
| ~ spl22_429 ),
inference(resolution,[],[f5992,f960]) ).
fof(f27440,plain,
( spl22_1113
| ~ spl22_116
| ~ spl22_428 ),
inference(avatar_split_clause,[],[f5987,f5954,f959,f27438]) ).
fof(f27438,plain,
( spl22_1113
<=> ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK19,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK19,X115),sK13(X115,X116,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1113])]) ).
fof(f5987,plain,
( ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK19,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK19,X115),sK13(X115,X116,sK15)) )
| ~ spl22_116
| ~ spl22_428 ),
inference(resolution,[],[f5955,f960]) ).
fof(f27436,plain,
( spl22_1112
| ~ spl22_116
| ~ spl22_427 ),
inference(avatar_split_clause,[],[f5950,f5917,f959,f27434]) ).
fof(f27434,plain,
( spl22_1112
<=> ! [X114,X115] :
( apply(relation_dom_restriction(sK15,X114),sK13(sK15,X115,X114)) = apply(sK15,sK13(sK15,X115,X114))
| sP2(sK15,X115,X114) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1112])]) ).
fof(f5950,plain,
( ! [X114,X115] :
( apply(relation_dom_restriction(sK15,X114),sK13(sK15,X115,X114)) = apply(sK15,sK13(sK15,X115,X114))
| sP2(sK15,X115,X114) )
| ~ spl22_116
| ~ spl22_427 ),
inference(resolution,[],[f5918,f960]) ).
fof(f27432,plain,
( spl22_1111
| ~ spl22_116
| ~ spl22_426 ),
inference(avatar_split_clause,[],[f5913,f5880,f959,f27430]) ).
fof(f27430,plain,
( spl22_1111
<=> ! [X114,X115] :
( sP2(sK15,X114,X115)
| apply(relation_dom_restriction(sK20,X115),sK13(sK15,X114,X115)) = apply(sK20,sK13(sK15,X114,X115)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1111])]) ).
fof(f5913,plain,
( ! [X114,X115] :
( sP2(sK15,X114,X115)
| apply(relation_dom_restriction(sK20,X115),sK13(sK15,X114,X115)) = apply(sK20,sK13(sK15,X114,X115)) )
| ~ spl22_116
| ~ spl22_426 ),
inference(resolution,[],[f5881,f960]) ).
fof(f27428,plain,
( spl22_1110
| ~ spl22_116
| ~ spl22_425 ),
inference(avatar_split_clause,[],[f5876,f5843,f959,f27426]) ).
fof(f27426,plain,
( spl22_1110
<=> ! [X114,X115] :
( sP2(sK15,X114,X115)
| apply(relation_dom_restriction(sK19,X115),sK13(sK15,X114,X115)) = apply(sK19,sK13(sK15,X114,X115)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1110])]) ).
fof(f5876,plain,
( ! [X114,X115] :
( sP2(sK15,X114,X115)
| apply(relation_dom_restriction(sK19,X115),sK13(sK15,X114,X115)) = apply(sK19,sK13(sK15,X114,X115)) )
| ~ spl22_116
| ~ spl22_425 ),
inference(resolution,[],[f5844,f960]) ).
fof(f27424,plain,
( ~ spl22_2
| ~ spl22_1
| ~ spl22_240
| spl22_1088 ),
inference(avatar_split_clause,[],[f27383,f27335,f2448,f219,f224]) ).
fof(f27335,plain,
( spl22_1088
<=> sP1(relation_dom_restriction(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1088])]) ).
fof(f27383,plain,
( ~ relation(sK5)
| ~ function(sK5)
| ~ spl22_240
| spl22_1088 ),
inference(resolution,[],[f27337,f2449]) ).
fof(f27337,plain,
( ~ sP1(relation_dom_restriction(sK5,sK15))
| spl22_1088 ),
inference(avatar_component_clause,[],[f27335]) ).
fof(f27423,plain,
( spl22_1109
| ~ spl22_116
| ~ spl22_423 ),
inference(avatar_split_clause,[],[f5834,f5801,f959,f27421]) ).
fof(f27421,plain,
( spl22_1109
<=> ! [X116,X115] :
( apply(sK15,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK15,X116),sK13(X115,X116,sK15))
| sP2(X115,X116,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1109])]) ).
fof(f5834,plain,
( ! [X116,X115] :
( apply(sK15,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK15,X116),sK13(X115,X116,sK15))
| sP2(X115,X116,sK15) )
| ~ spl22_116
| ~ spl22_423 ),
inference(resolution,[],[f5802,f960]) ).
fof(f27419,plain,
( spl22_1108
| ~ spl22_116
| ~ spl22_422 ),
inference(avatar_split_clause,[],[f5797,f5764,f959,f27417]) ).
fof(f27417,plain,
( spl22_1108
<=> ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK20,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK20,X116),sK13(X115,X116,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1108])]) ).
fof(f5797,plain,
( ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK20,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK20,X116),sK13(X115,X116,sK15)) )
| ~ spl22_116
| ~ spl22_422 ),
inference(resolution,[],[f5765,f960]) ).
fof(f27415,plain,
( spl22_1107
| ~ spl22_116
| ~ spl22_421 ),
inference(avatar_split_clause,[],[f5760,f5727,f959,f27413]) ).
fof(f27413,plain,
( spl22_1107
<=> ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK19,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK19,X116),sK13(X115,X116,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1107])]) ).
fof(f5760,plain,
( ! [X116,X115] :
( sP2(X115,X116,sK15)
| apply(sK19,sK13(X115,X116,sK15)) = apply(relation_dom_restriction(sK19,X116),sK13(X115,X116,sK15)) )
| ~ spl22_116
| ~ spl22_421 ),
inference(resolution,[],[f5728,f960]) ).
fof(f27411,plain,
( spl22_1106
| ~ spl22_116
| ~ spl22_420 ),
inference(avatar_split_clause,[],[f5723,f5690,f959,f27409]) ).
fof(f27409,plain,
( spl22_1106
<=> ! [X116,X115] :
( apply(relation_dom_restriction(sK15,X115),sK13(X116,sK15,X115)) = apply(sK15,sK13(X116,sK15,X115))
| sP2(X116,sK15,X115) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1106])]) ).
fof(f5723,plain,
( ! [X116,X115] :
( apply(relation_dom_restriction(sK15,X115),sK13(X116,sK15,X115)) = apply(sK15,sK13(X116,sK15,X115))
| sP2(X116,sK15,X115) )
| ~ spl22_116
| ~ spl22_420 ),
inference(resolution,[],[f5691,f960]) ).
fof(f27407,plain,
( spl22_1105
| ~ spl22_116
| ~ spl22_419 ),
inference(avatar_split_clause,[],[f5686,f5653,f959,f27405]) ).
fof(f27405,plain,
( spl22_1105
<=> ! [X116,X115] :
( sP2(X115,sK15,X116)
| apply(relation_dom_restriction(sK20,X116),sK13(X115,sK15,X116)) = apply(sK20,sK13(X115,sK15,X116)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1105])]) ).
fof(f5686,plain,
( ! [X116,X115] :
( sP2(X115,sK15,X116)
| apply(relation_dom_restriction(sK20,X116),sK13(X115,sK15,X116)) = apply(sK20,sK13(X115,sK15,X116)) )
| ~ spl22_116
| ~ spl22_419 ),
inference(resolution,[],[f5654,f960]) ).
fof(f27403,plain,
( spl22_1104
| ~ spl22_116
| ~ spl22_418 ),
inference(avatar_split_clause,[],[f5598,f5566,f959,f27401]) ).
fof(f27401,plain,
( spl22_1104
<=> ! [X114,X113] :
( sP2(X113,sK15,X114)
| apply(relation_dom_restriction(sK19,X114),sK13(X113,sK15,X114)) = apply(sK19,sK13(X113,sK15,X114)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1104])]) ).
fof(f5598,plain,
( ! [X113,X114] :
( sP2(X113,sK15,X114)
| apply(relation_dom_restriction(sK19,X114),sK13(X113,sK15,X114)) = apply(sK19,sK13(X113,sK15,X114)) )
| ~ spl22_116
| ~ spl22_418 ),
inference(resolution,[],[f5567,f960]) ).
fof(f27399,plain,
( spl22_1103
| ~ spl22_41
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5217,f5211,f414,f27397]) ).
fof(f27397,plain,
( spl22_1103
<=> ! [X9,X8] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK15,X9),sK7(X8,X9)) = apply(sK15,sK7(X8,X9))
| ~ empty(relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1103])]) ).
fof(f5217,plain,
( ! [X8,X9] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK15,X9),sK7(X8,X9)) = apply(sK15,sK7(X8,X9))
| ~ empty(relation_dom(X8)) )
| ~ spl22_41
| ~ spl22_405 ),
inference(resolution,[],[f5212,f415]) ).
fof(f27395,plain,
( spl22_1102
| ~ spl22_236
| ~ spl22_405 ),
inference(avatar_split_clause,[],[f5216,f5211,f2331,f27393]) ).
fof(f27393,plain,
( spl22_1102
<=> ! [X6,X7] :
( sP0(X6,X7)
| apply(relation_dom_restriction(sK15,X7),sK7(X6,X7)) = apply(sK15,sK7(X6,X7))
| ~ sP0(X6,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1102])]) ).
fof(f5216,plain,
( ! [X6,X7] :
( sP0(X6,X7)
| apply(relation_dom_restriction(sK15,X7),sK7(X6,X7)) = apply(sK15,sK7(X6,X7))
| ~ sP0(X6,sK15) )
| ~ spl22_236
| ~ spl22_405 ),
inference(resolution,[],[f5212,f2332]) ).
fof(f27391,plain,
( spl22_1101
| ~ spl22_41
| ~ spl22_403 ),
inference(avatar_split_clause,[],[f5205,f5195,f414,f27389]) ).
fof(f27389,plain,
( spl22_1101
<=> ! [X9,X8] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK20,X9),sK7(X8,X9)) = apply(sK20,sK7(X8,X9))
| ~ empty(relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1101])]) ).
fof(f5205,plain,
( ! [X8,X9] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK20,X9),sK7(X8,X9)) = apply(sK20,sK7(X8,X9))
| ~ empty(relation_dom(X8)) )
| ~ spl22_41
| ~ spl22_403 ),
inference(resolution,[],[f5196,f415]) ).
fof(f27387,plain,
( spl22_1100
| ~ spl22_236
| ~ spl22_403 ),
inference(avatar_split_clause,[],[f5204,f5195,f2331,f27385]) ).
fof(f27385,plain,
( spl22_1100
<=> ! [X6,X7] :
( sP0(X6,X7)
| apply(relation_dom_restriction(sK20,X7),sK7(X6,X7)) = apply(sK20,sK7(X6,X7))
| ~ sP0(X6,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1100])]) ).
fof(f5204,plain,
( ! [X6,X7] :
( sP0(X6,X7)
| apply(relation_dom_restriction(sK20,X7),sK7(X6,X7)) = apply(sK20,sK7(X6,X7))
| ~ sP0(X6,sK15) )
| ~ spl22_236
| ~ spl22_403 ),
inference(resolution,[],[f5196,f2332]) ).
fof(f27382,plain,
( spl22_1099
| ~ spl22_41
| ~ spl22_402 ),
inference(avatar_split_clause,[],[f5189,f5183,f414,f27380]) ).
fof(f27380,plain,
( spl22_1099
<=> ! [X9,X8] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK19,X9),sK7(X8,X9)) = apply(sK19,sK7(X8,X9))
| ~ empty(relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1099])]) ).
fof(f5189,plain,
( ! [X8,X9] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK19,X9),sK7(X8,X9)) = apply(sK19,sK7(X8,X9))
| ~ empty(relation_dom(X8)) )
| ~ spl22_41
| ~ spl22_402 ),
inference(resolution,[],[f5184,f415]) ).
fof(f27378,plain,
( spl22_1098
| ~ spl22_236
| ~ spl22_402 ),
inference(avatar_split_clause,[],[f5188,f5183,f2331,f27376]) ).
fof(f27376,plain,
( spl22_1098
<=> ! [X6,X7] :
( sP0(X6,X7)
| apply(relation_dom_restriction(sK19,X7),sK7(X6,X7)) = apply(sK19,sK7(X6,X7))
| ~ sP0(X6,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1098])]) ).
fof(f5188,plain,
( ! [X6,X7] :
( sP0(X6,X7)
| apply(relation_dom_restriction(sK19,X7),sK7(X6,X7)) = apply(sK19,sK7(X6,X7))
| ~ sP0(X6,sK15) )
| ~ spl22_236
| ~ spl22_402 ),
inference(resolution,[],[f5184,f2332]) ).
fof(f27374,plain,
( spl22_1097
| ~ spl22_41
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5156,f5153,f414,f27372]) ).
fof(f27372,plain,
( spl22_1097
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1097])]) ).
fof(f5156,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK15,relation_dom(X0)),sK8(X0,X1)) = apply(sK15,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_401 ),
inference(resolution,[],[f5154,f415]) ).
fof(f27370,plain,
( spl22_1096
| ~ spl22_41
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5126,f5123,f414,f27368]) ).
fof(f27368,plain,
( spl22_1096
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1096])]) ).
fof(f5126,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK20,relation_dom(X0)),sK8(X0,X1)) = apply(sK20,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_400 ),
inference(resolution,[],[f5124,f415]) ).
fof(f27366,plain,
( spl22_1095
| ~ spl22_41
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5096,f5093,f414,f27364]) ).
fof(f27364,plain,
( spl22_1095
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1095])]) ).
fof(f5096,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK19,relation_dom(X0)),sK8(X0,X1)) = apply(sK19,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_399 ),
inference(resolution,[],[f5094,f415]) ).
fof(f27362,plain,
( spl22_1094
| ~ spl22_236
| ~ spl22_379 ),
inference(avatar_split_clause,[],[f4699,f4558,f2331,f27360]) ).
fof(f27360,plain,
( spl22_1094
<=> ! [X38,X36,X37] :
( element(sK13(sK10(powerset(X36)),X37,relation_dom(X38)),X36)
| sP2(sK10(powerset(X36)),X37,relation_dom(X38))
| ~ sP0(X38,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1094])]) ).
fof(f4699,plain,
( ! [X38,X36,X37] :
( element(sK13(sK10(powerset(X36)),X37,relation_dom(X38)),X36)
| sP2(sK10(powerset(X36)),X37,relation_dom(X38))
| ~ sP0(X38,sK15) )
| ~ spl22_236
| ~ spl22_379 ),
inference(resolution,[],[f4559,f2332]) ).
fof(f27358,plain,
( spl22_1093
| ~ spl22_236
| ~ spl22_378 ),
inference(avatar_split_clause,[],[f4670,f4554,f2331,f27356]) ).
fof(f27356,plain,
( spl22_1093
<=> ! [X38,X36,X37] :
( element(sK13(X36,sK10(powerset(X37)),relation_dom(X38)),X37)
| sP2(X36,sK10(powerset(X37)),relation_dom(X38))
| ~ sP0(X38,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1093])]) ).
fof(f4670,plain,
( ! [X38,X36,X37] :
( element(sK13(X36,sK10(powerset(X37)),relation_dom(X38)),X37)
| sP2(X36,sK10(powerset(X37)),relation_dom(X38))
| ~ sP0(X38,sK15) )
| ~ spl22_236
| ~ spl22_378 ),
inference(resolution,[],[f4555,f2332]) ).
fof(f27354,plain,
( spl22_1092
| ~ spl22_236
| ~ spl22_377 ),
inference(avatar_split_clause,[],[f4641,f4550,f2331,f27352]) ).
fof(f27352,plain,
( spl22_1092
<=> ! [X38,X36,X37] :
( element(sK13(X36,relation_dom(X37),sK10(powerset(X38))),X38)
| sP2(X36,relation_dom(X37),sK10(powerset(X38)))
| ~ sP0(X37,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1092])]) ).
fof(f4641,plain,
( ! [X38,X36,X37] :
( element(sK13(X36,relation_dom(X37),sK10(powerset(X38))),X38)
| sP2(X36,relation_dom(X37),sK10(powerset(X38)))
| ~ sP0(X37,sK15) )
| ~ spl22_236
| ~ spl22_377 ),
inference(resolution,[],[f4551,f2332]) ).
fof(f27350,plain,
( spl22_1091
| ~ spl22_236
| ~ spl22_376 ),
inference(avatar_split_clause,[],[f4612,f4546,f2331,f27348]) ).
fof(f27348,plain,
( spl22_1091
<=> ! [X36,X37,X35] :
( element(sK13(relation_dom(X35),X36,sK10(powerset(X37))),X37)
| sP2(relation_dom(X35),X36,sK10(powerset(X37)))
| ~ sP0(X35,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1091])]) ).
fof(f4612,plain,
( ! [X36,X37,X35] :
( element(sK13(relation_dom(X35),X36,sK10(powerset(X37))),X37)
| sP2(relation_dom(X35),X36,sK10(powerset(X37)))
| ~ sP0(X35,sK15) )
| ~ spl22_236
| ~ spl22_376 ),
inference(resolution,[],[f4547,f2332]) ).
fof(f27346,plain,
( spl22_1090
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_366 ),
inference(avatar_split_clause,[],[f4293,f4135,f812,f249,f433,f27344]) ).
fof(f27344,plain,
( spl22_1090
<=> ! [X10] :
( apply(relation_dom_restriction(sK15,powerset(X10)),sK6(X10)) = apply(sK15,sK6(X10))
| empty(powerset(X10))
| empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1090])]) ).
fof(f4293,plain,
( ! [X10] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,powerset(X10)),sK6(X10)) = apply(sK15,sK6(X10))
| empty(X10)
| empty(powerset(X10)) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_366 ),
inference(forward_demodulation,[],[f4292,f814]) ).
fof(f4292,plain,
( ! [X10] :
( apply(relation_dom_restriction(sK15,powerset(X10)),sK6(X10)) = apply(sK15,sK6(X10))
| empty(X10)
| ~ function(empty_set)
| empty(powerset(X10)) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_366 ),
inference(forward_demodulation,[],[f4283,f814]) ).
fof(f4283,plain,
( ! [X10] :
( empty(X10)
| apply(relation_dom_restriction(empty_set,powerset(X10)),sK6(X10)) = apply(empty_set,sK6(X10))
| ~ function(empty_set)
| empty(powerset(X10)) )
| ~ spl22_7
| ~ spl22_366 ),
inference(resolution,[],[f4136,f251]) ).
fof(f27342,plain,
( ~ spl22_1088
| spl22_1089
| ~ spl22_62
| ~ spl22_1023 ),
inference(avatar_split_clause,[],[f25445,f25336,f598,f27339,f27335]) ).
fof(f25336,plain,
( spl22_1023
<=> sP0(relation_dom_restriction(sK5,sK15),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1023])]) ).
fof(f25445,plain,
( sK15 = relation_rng(relation_dom_restriction(sK5,sK15))
| ~ sP1(relation_dom_restriction(sK5,sK15))
| ~ spl22_62
| ~ spl22_1023 ),
inference(resolution,[],[f25338,f599]) ).
fof(f25338,plain,
( sP0(relation_dom_restriction(sK5,sK15),sK15)
| ~ spl22_1023 ),
inference(avatar_component_clause,[],[f25336]) ).
fof(f27265,plain,
( ~ spl22_20
| spl22_1087
| ~ spl22_19
| ~ spl22_366 ),
inference(avatar_split_clause,[],[f4290,f4135,f309,f27263,f314]) ).
fof(f27263,plain,
( spl22_1087
<=> ! [X17] :
( empty(X17)
| empty(powerset(X17))
| apply(relation_dom_restriction(sK20,powerset(X17)),sK6(X17)) = apply(sK20,sK6(X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1087])]) ).
fof(f4290,plain,
( ! [X17] :
( empty(X17)
| apply(relation_dom_restriction(sK20,powerset(X17)),sK6(X17)) = apply(sK20,sK6(X17))
| ~ function(sK20)
| empty(powerset(X17)) )
| ~ spl22_19
| ~ spl22_366 ),
inference(resolution,[],[f4136,f311]) ).
fof(f27193,plain,
( ~ spl22_18
| spl22_1086
| ~ spl22_17
| ~ spl22_366 ),
inference(avatar_split_clause,[],[f4289,f4135,f299,f27191,f304]) ).
fof(f27191,plain,
( spl22_1086
<=> ! [X16] :
( empty(X16)
| empty(powerset(X16))
| apply(relation_dom_restriction(sK19,powerset(X16)),sK6(X16)) = apply(sK19,sK6(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1086])]) ).
fof(f4289,plain,
( ! [X16] :
( empty(X16)
| apply(relation_dom_restriction(sK19,powerset(X16)),sK6(X16)) = apply(sK19,sK6(X16))
| ~ function(sK19)
| empty(powerset(X16)) )
| ~ spl22_17
| ~ spl22_366 ),
inference(resolution,[],[f4136,f301]) ).
fof(f27189,plain,
( spl22_1085
| ~ spl22_236
| ~ spl22_365 ),
inference(avatar_split_clause,[],[f4268,f4131,f2331,f27187]) ).
fof(f27187,plain,
( spl22_1085
<=> ! [X38,X36,X37] :
( element(sK13(sK6(X36),X37,relation_dom(X38)),X36)
| empty(X36)
| sP2(sK6(X36),X37,relation_dom(X38))
| ~ sP0(X38,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1085])]) ).
fof(f4268,plain,
( ! [X38,X36,X37] :
( element(sK13(sK6(X36),X37,relation_dom(X38)),X36)
| empty(X36)
| sP2(sK6(X36),X37,relation_dom(X38))
| ~ sP0(X38,sK15) )
| ~ spl22_236
| ~ spl22_365 ),
inference(resolution,[],[f4132,f2332]) ).
fof(f27185,plain,
( spl22_1084
| ~ spl22_236
| ~ spl22_364 ),
inference(avatar_split_clause,[],[f4242,f4127,f2331,f27183]) ).
fof(f27183,plain,
( spl22_1084
<=> ! [X38,X36,X37] :
( element(sK13(X36,sK6(X37),relation_dom(X38)),X37)
| empty(X37)
| sP2(X36,sK6(X37),relation_dom(X38))
| ~ sP0(X38,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1084])]) ).
fof(f4242,plain,
( ! [X38,X36,X37] :
( element(sK13(X36,sK6(X37),relation_dom(X38)),X37)
| empty(X37)
| sP2(X36,sK6(X37),relation_dom(X38))
| ~ sP0(X38,sK15) )
| ~ spl22_236
| ~ spl22_364 ),
inference(resolution,[],[f4128,f2332]) ).
fof(f27181,plain,
( spl22_1083
| ~ spl22_236
| ~ spl22_363 ),
inference(avatar_split_clause,[],[f4216,f4123,f2331,f27179]) ).
fof(f27179,plain,
( spl22_1083
<=> ! [X38,X36,X37] :
( element(sK13(X36,relation_dom(X37),sK6(X38)),X38)
| empty(X38)
| sP2(X36,relation_dom(X37),sK6(X38))
| ~ sP0(X37,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1083])]) ).
fof(f4216,plain,
( ! [X38,X36,X37] :
( element(sK13(X36,relation_dom(X37),sK6(X38)),X38)
| empty(X38)
| sP2(X36,relation_dom(X37),sK6(X38))
| ~ sP0(X37,sK15) )
| ~ spl22_236
| ~ spl22_363 ),
inference(resolution,[],[f4124,f2332]) ).
fof(f27177,plain,
( spl22_1082
| ~ spl22_236
| ~ spl22_362 ),
inference(avatar_split_clause,[],[f4190,f4119,f2331,f27175]) ).
fof(f27175,plain,
( spl22_1082
<=> ! [X36,X37,X35] :
( element(sK13(relation_dom(X35),X36,sK6(X37)),X37)
| empty(X37)
| sP2(relation_dom(X35),X36,sK6(X37))
| ~ sP0(X35,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1082])]) ).
fof(f4190,plain,
( ! [X36,X37,X35] :
( element(sK13(relation_dom(X35),X36,sK6(X37)),X37)
| empty(X37)
| sP2(relation_dom(X35),X36,sK6(X37))
| ~ sP0(X35,sK15) )
| ~ spl22_236
| ~ spl22_362 ),
inference(resolution,[],[f4120,f2332]) ).
fof(f27173,plain,
( spl22_1081
| ~ spl22_197
| ~ spl22_359 ),
inference(avatar_split_clause,[],[f4080,f4035,f1926,f27171]) ).
fof(f27171,plain,
( spl22_1081
<=> ! [X0] :
( element(sK8(sK15,sK10(powerset(X0))),sK15)
| element(sK7(sK15,sK10(powerset(X0))),X0)
| sP0(sK15,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1081])]) ).
fof(f4080,plain,
( ! [X0] :
( element(sK8(sK15,sK10(powerset(X0))),sK15)
| element(sK7(sK15,sK10(powerset(X0))),X0)
| sP0(sK15,sK10(powerset(X0))) )
| ~ spl22_197
| ~ spl22_359 ),
inference(superposition,[],[f4036,f1928]) ).
fof(f27169,plain,
( spl22_1080
| ~ spl22_197
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4065,f4027,f1926,f27167]) ).
fof(f27167,plain,
( spl22_1080
<=> ! [X0] :
( in(sK8(sK15,sK10(powerset(X0))),sK15)
| element(sK7(sK15,sK10(powerset(X0))),X0)
| sP0(sK15,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1080])]) ).
fof(f4065,plain,
( ! [X0] :
( in(sK8(sK15,sK10(powerset(X0))),sK15)
| element(sK7(sK15,sK10(powerset(X0))),X0)
| sP0(sK15,sK10(powerset(X0))) )
| ~ spl22_197
| ~ spl22_357 ),
inference(superposition,[],[f4028,f1928]) ).
fof(f27165,plain,
( spl22_1079
| ~ spl22_114
| ~ spl22_961 ),
inference(avatar_split_clause,[],[f22915,f20558,f952,f27163]) ).
fof(f27163,plain,
( spl22_1079
<=> ! [X6] :
( ~ empty(relation_dom_restriction(sK5,X6))
| sK15 = set_intersection2(X6,relation_dom(sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1079])]) ).
fof(f22915,plain,
( ! [X6] :
( ~ empty(relation_dom_restriction(sK5,X6))
| sK15 = set_intersection2(X6,relation_dom(sK5)) )
| ~ spl22_114
| ~ spl22_961 ),
inference(resolution,[],[f20559,f953]) ).
fof(f27161,plain,
( spl22_1078
| ~ spl22_283
| ~ spl22_356 ),
inference(avatar_split_clause,[],[f4048,f4023,f2979,f27159]) ).
fof(f27159,plain,
( spl22_1078
<=> ! [X4,X5,X3] :
( sK7(X3,sK10(powerset(X4))) = apply(X3,sK8(X3,sK10(powerset(X4))))
| ~ empty(X4)
| ~ in(X5,relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1078])]) ).
fof(f2979,plain,
( spl22_283
<=> ! [X20,X21,X19] :
( ~ in(X19,relation_dom(X20))
| ~ sP0(X20,sK10(powerset(X21)))
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_283])]) ).
fof(f4048,plain,
( ! [X3,X4,X5] :
( sK7(X3,sK10(powerset(X4))) = apply(X3,sK8(X3,sK10(powerset(X4))))
| ~ empty(X4)
| ~ in(X5,relation_dom(X3)) )
| ~ spl22_283
| ~ spl22_356 ),
inference(duplicate_literal_removal,[],[f4043]) ).
fof(f4043,plain,
( ! [X3,X4,X5] :
( sK7(X3,sK10(powerset(X4))) = apply(X3,sK8(X3,sK10(powerset(X4))))
| ~ empty(X4)
| ~ in(X5,relation_dom(X3))
| ~ empty(X4) )
| ~ spl22_283
| ~ spl22_356 ),
inference(resolution,[],[f4024,f2980]) ).
fof(f2980,plain,
( ! [X21,X19,X20] :
( ~ sP0(X20,sK10(powerset(X21)))
| ~ in(X19,relation_dom(X20))
| ~ empty(X21) )
| ~ spl22_283 ),
inference(avatar_component_clause,[],[f2979]) ).
fof(f27157,plain,
( spl22_1077
| ~ spl22_250
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4012,f3873,f2571,f27155]) ).
fof(f27155,plain,
( spl22_1077
<=> ! [X35,X34,X33,X32] :
( subset(sK13(powerset(X32),X33,relation_dom(X34)),X32)
| sP2(powerset(X32),X33,relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1077])]) ).
fof(f4012,plain,
( ! [X34,X35,X32,X33] :
( subset(sK13(powerset(X32),X33,relation_dom(X34)),X32)
| sP2(powerset(X32),X33,relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_354 ),
inference(resolution,[],[f3874,f2572]) ).
fof(f27153,plain,
( spl22_1076
| ~ spl22_45
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4007,f3873,f448,f27151]) ).
fof(f27151,plain,
( spl22_1076
<=> ! [X16,X14,X15] :
( subset(sK13(powerset(X14),X15,X16),X14)
| sP2(powerset(X14),X15,X16)
| ~ in(X16,sK13(powerset(X14),X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1076])]) ).
fof(f4007,plain,
( ! [X16,X14,X15] :
( subset(sK13(powerset(X14),X15,X16),X14)
| sP2(powerset(X14),X15,X16)
| ~ in(X16,sK13(powerset(X14),X15,X16)) )
| ~ spl22_45
| ~ spl22_354 ),
inference(resolution,[],[f3874,f449]) ).
fof(f27149,plain,
( spl22_1075
| ~ spl22_250
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3990,f3869,f2571,f27147]) ).
fof(f27147,plain,
( spl22_1075
<=> ! [X31,X34,X33,X32] :
( subset(sK13(relation_dom(X31),X32,powerset(X33)),X33)
| sP2(relation_dom(X31),X32,powerset(X33))
| ~ sP0(X31,X34)
| ~ empty(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1075])]) ).
fof(f3990,plain,
( ! [X31,X34,X32,X33] :
( subset(sK13(relation_dom(X31),X32,powerset(X33)),X33)
| sP2(relation_dom(X31),X32,powerset(X33))
| ~ sP0(X31,X34)
| ~ empty(X34) )
| ~ spl22_250
| ~ spl22_353 ),
inference(resolution,[],[f3870,f2572]) ).
fof(f27145,plain,
( spl22_1074
| ~ spl22_45
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3985,f3869,f448,f27143]) ).
fof(f27143,plain,
( spl22_1074
<=> ! [X13,X14,X15] :
( subset(sK13(X13,X14,powerset(X15)),X15)
| sP2(X13,X14,powerset(X15))
| ~ in(X13,sK13(X13,X14,powerset(X15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1074])]) ).
fof(f3985,plain,
( ! [X14,X15,X13] :
( subset(sK13(X13,X14,powerset(X15)),X15)
| sP2(X13,X14,powerset(X15))
| ~ in(X13,sK13(X13,X14,powerset(X15))) )
| ~ spl22_45
| ~ spl22_353 ),
inference(resolution,[],[f3870,f449]) ).
fof(f27141,plain,
( spl22_1073
| ~ spl22_250
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3968,f3865,f2571,f27139]) ).
fof(f27139,plain,
( spl22_1073
<=> ! [X35,X34,X33,X32] :
( subset(sK13(X32,powerset(X33),relation_dom(X34)),X33)
| sP2(X32,powerset(X33),relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1073])]) ).
fof(f3968,plain,
( ! [X34,X35,X32,X33] :
( subset(sK13(X32,powerset(X33),relation_dom(X34)),X33)
| sP2(X32,powerset(X33),relation_dom(X34))
| ~ sP0(X34,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_352 ),
inference(resolution,[],[f3866,f2572]) ).
fof(f27137,plain,
( spl22_1072
| ~ spl22_45
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3963,f3865,f448,f27135]) ).
fof(f27135,plain,
( spl22_1072
<=> ! [X16,X14,X15] :
( subset(sK13(X14,powerset(X15),X16),X15)
| sP2(X14,powerset(X15),X16)
| ~ in(X16,sK13(X14,powerset(X15),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1072])]) ).
fof(f3963,plain,
( ! [X16,X14,X15] :
( subset(sK13(X14,powerset(X15),X16),X15)
| sP2(X14,powerset(X15),X16)
| ~ in(X16,sK13(X14,powerset(X15),X16)) )
| ~ spl22_45
| ~ spl22_352 ),
inference(resolution,[],[f3866,f449]) ).
fof(f27133,plain,
( spl22_1071
| ~ spl22_250
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3946,f3861,f2571,f27131]) ).
fof(f27131,plain,
( spl22_1071
<=> ! [X35,X34,X33,X32] :
( subset(sK13(X32,relation_dom(X33),powerset(X34)),X34)
| sP2(X32,relation_dom(X33),powerset(X34))
| ~ sP0(X33,X35)
| ~ empty(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1071])]) ).
fof(f3946,plain,
( ! [X34,X35,X32,X33] :
( subset(sK13(X32,relation_dom(X33),powerset(X34)),X34)
| sP2(X32,relation_dom(X33),powerset(X34))
| ~ sP0(X33,X35)
| ~ empty(X35) )
| ~ spl22_250
| ~ spl22_351 ),
inference(resolution,[],[f3862,f2572]) ).
fof(f27129,plain,
( spl22_1070
| ~ spl22_45
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3941,f3861,f448,f27127]) ).
fof(f27127,plain,
( spl22_1070
<=> ! [X16,X14,X15] :
( subset(sK13(X14,X15,powerset(X16)),X16)
| sP2(X14,X15,powerset(X16))
| ~ in(X15,sK13(X14,X15,powerset(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1070])]) ).
fof(f3941,plain,
( ! [X16,X14,X15] :
( subset(sK13(X14,X15,powerset(X16)),X16)
| sP2(X14,X15,powerset(X16))
| ~ in(X15,sK13(X14,X15,powerset(X16))) )
| ~ spl22_45
| ~ spl22_351 ),
inference(resolution,[],[f3862,f449]) ).
fof(f27125,plain,
( spl22_1069
| ~ spl22_56
| ~ spl22_349 ),
inference(avatar_split_clause,[],[f3895,f3853,f540,f27123]) ).
fof(f27123,plain,
( spl22_1069
<=> ! [X9,X8] :
( element(sK8(X8,sK6(X9)),relation_dom(X8))
| sP0(X8,sK6(X9))
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1069])]) ).
fof(f3895,plain,
( ! [X8,X9] :
( element(sK8(X8,sK6(X9)),relation_dom(X8))
| sP0(X8,sK6(X9))
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_349 ),
inference(duplicate_literal_removal,[],[f3893]) ).
fof(f3893,plain,
( ! [X8,X9] :
( element(sK8(X8,sK6(X9)),relation_dom(X8))
| sP0(X8,sK6(X9))
| empty(X9)
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_349 ),
inference(resolution,[],[f3854,f541]) ).
fof(f27112,plain,
( spl22_1068
| ~ spl22_56
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3888,f3849,f540,f27110]) ).
fof(f27110,plain,
( spl22_1068
<=> ! [X9,X8] :
( in(sK8(X8,sK6(X9)),relation_dom(X8))
| empty(X9)
| sP0(X8,sK6(X9))
| in(sK7(X8,sK6(X9)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1068])]) ).
fof(f3888,plain,
( ! [X8,X9] :
( in(sK8(X8,sK6(X9)),relation_dom(X8))
| empty(X9)
| sP0(X8,sK6(X9))
| in(sK7(X8,sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_348 ),
inference(duplicate_literal_removal,[],[f3886]) ).
fof(f3886,plain,
( ! [X8,X9] :
( in(sK8(X8,sK6(X9)),relation_dom(X8))
| empty(X9)
| sP0(X8,sK6(X9))
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_348 ),
inference(resolution,[],[f3850,f541]) ).
fof(f27108,plain,
( spl22_1067
| ~ spl22_45
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3882,f3849,f448,f27106]) ).
fof(f27106,plain,
( spl22_1067
<=> ! [X16,X15] :
( element(sK7(X15,sK6(X16)),X16)
| empty(X16)
| sP0(X15,sK6(X16))
| ~ in(relation_dom(X15),sK8(X15,sK6(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1067])]) ).
fof(f3882,plain,
( ! [X16,X15] :
( element(sK7(X15,sK6(X16)),X16)
| empty(X16)
| sP0(X15,sK6(X16))
| ~ in(relation_dom(X15),sK8(X15,sK6(X16))) )
| ~ spl22_45
| ~ spl22_348 ),
inference(resolution,[],[f3850,f449]) ).
fof(f27104,plain,
( spl22_1066
| ~ spl22_52
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f3726,f3433,f498,f27102]) ).
fof(f27102,plain,
( spl22_1066
<=> ! [X9,X8,X10] :
( element(sK13(powerset(X8),X9,X10),X10)
| sP2(powerset(X8),X9,X10)
| subset(sK13(powerset(X8),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1066])]) ).
fof(f3726,plain,
( ! [X10,X8,X9] :
( element(sK13(powerset(X8),X9,X10),X10)
| sP2(powerset(X8),X9,X10)
| subset(sK13(powerset(X8),X9,X10),X8) )
| ~ spl22_52
| ~ spl22_333 ),
inference(resolution,[],[f3434,f499]) ).
fof(f27100,plain,
( spl22_1065
| ~ spl22_52
| ~ spl22_333 ),
inference(avatar_split_clause,[],[f3722,f3433,f498,f27098]) ).
fof(f27098,plain,
( spl22_1065
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,powerset(X10)),X8)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1065])]) ).
fof(f3722,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,powerset(X10)),X8)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_333 ),
inference(resolution,[],[f3434,f499]) ).
fof(f27096,plain,
( spl22_1064
| ~ spl22_52
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3703,f3396,f498,f27094]) ).
fof(f27094,plain,
( spl22_1064
<=> ! [X9,X8,X10] :
( element(sK13(X8,powerset(X9),X10),X10)
| sP2(X8,powerset(X9),X10)
| subset(sK13(X8,powerset(X9),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1064])]) ).
fof(f3703,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,powerset(X9),X10),X10)
| sP2(X8,powerset(X9),X10)
| subset(sK13(X8,powerset(X9),X10),X9) )
| ~ spl22_52
| ~ spl22_328 ),
inference(resolution,[],[f3397,f499]) ).
fof(f27092,plain,
( spl22_1063
| ~ spl22_52
| ~ spl22_328 ),
inference(avatar_split_clause,[],[f3699,f3396,f498,f27090]) ).
fof(f27090,plain,
( spl22_1063
<=> ! [X9,X8,X10] :
( element(sK13(X8,X9,powerset(X10)),X9)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1063])]) ).
fof(f3699,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,powerset(X10)),X9)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_328 ),
inference(resolution,[],[f3397,f499]) ).
fof(f27088,plain,
( spl22_1062
| ~ spl22_52
| ~ spl22_326 ),
inference(avatar_split_clause,[],[f3690,f3388,f498,f27086]) ).
fof(f27086,plain,
( spl22_1062
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X8,X9,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1062])]) ).
fof(f3690,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X8,X9,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X8,X9,sK6(powerset(X10))),X10) )
| ~ spl22_52
| ~ spl22_326 ),
inference(resolution,[],[f3389,f499]) ).
fof(f27084,plain,
( spl22_1061
| ~ spl22_52
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3681,f3380,f498,f27082]) ).
fof(f27082,plain,
( spl22_1061
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(sK6(powerset(X9)),X10,X8)
| empty(powerset(X9))
| subset(sK13(sK6(powerset(X9)),X10,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1061])]) ).
fof(f3681,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(sK6(powerset(X9)),X10,X8)
| empty(powerset(X9))
| subset(sK13(sK6(powerset(X9)),X10,X8),X9) )
| ~ spl22_52
| ~ spl22_324 ),
inference(resolution,[],[f3381,f499]) ).
fof(f27080,plain,
( spl22_1060
| ~ spl22_52
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3664,f3372,f498,f27078]) ).
fof(f27078,plain,
( spl22_1060
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X9,X8,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X9,X8,sK6(powerset(X10))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1060])]) ).
fof(f3664,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X9,X8,sK6(powerset(X10)))
| empty(powerset(X10))
| subset(sK13(X9,X8,sK6(powerset(X10))),X10) )
| ~ spl22_52
| ~ spl22_322 ),
inference(resolution,[],[f3373,f499]) ).
fof(f27076,plain,
( spl22_1059
| ~ spl22_52
| ~ spl22_320 ),
inference(avatar_split_clause,[],[f3655,f3364,f498,f27074]) ).
fof(f27074,plain,
( spl22_1059
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X9,sK6(powerset(X10)),X8)
| empty(powerset(X10))
| subset(sK13(X9,sK6(powerset(X10)),X8),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1059])]) ).
fof(f3655,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X9,sK6(powerset(X10)),X8)
| empty(powerset(X10))
| subset(sK13(X9,sK6(powerset(X10)),X8),X10) )
| ~ spl22_52
| ~ spl22_320 ),
inference(resolution,[],[f3365,f499]) ).
fof(f27068,plain,
( spl22_1058
| ~ spl22_65
| ~ spl22_309 ),
inference(avatar_split_clause,[],[f3296,f3268,f610,f27066]) ).
fof(f27066,plain,
( spl22_1058
<=> ! [X2,X0,X1,X3] :
( ~ sP0(X0,sK6(powerset(X1)))
| ~ in(X2,relation_dom(X0))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1058])]) ).
fof(f3296,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK6(powerset(X1)))
| ~ in(X2,relation_dom(X0))
| empty(powerset(X1))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) )
| ~ spl22_65
| ~ spl22_309 ),
inference(resolution,[],[f3269,f611]) ).
fof(f27064,plain,
( spl22_1057
| ~ spl22_65
| ~ spl22_308 ),
inference(avatar_split_clause,[],[f3288,f3264,f610,f27062]) ).
fof(f27062,plain,
( spl22_1057
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1057])]) ).
fof(f3288,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,sK10(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X2,sK7(X0,sK10(powerset(powerset(X1))))) )
| ~ spl22_65
| ~ spl22_308 ),
inference(resolution,[],[f3265,f611]) ).
fof(f27060,plain,
( spl22_1056
| ~ spl22_65
| ~ spl22_302 ),
inference(avatar_split_clause,[],[f3244,f3229,f610,f27058]) ).
fof(f27058,plain,
( spl22_1056
<=> ! [X2,X0,X1] :
( element(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1056])]) ).
fof(f3244,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_302 ),
inference(resolution,[],[f3230,f611]) ).
fof(f27056,plain,
( spl22_1055
| ~ spl22_153
| ~ spl22_280 ),
inference(avatar_split_clause,[],[f3006,f2967,f1395,f27054]) ).
fof(f27054,plain,
( spl22_1055
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,apply(X1,X2))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK7(X0,apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1055])]) ).
fof(f2967,plain,
( spl22_280
<=> ! [X8,X7] :
( sP0(X7,X8)
| ~ empty(relation_dom(X7))
| ~ in(X8,sK7(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_280])]) ).
fof(f3006,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,apply(X1,X2))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK7(X0,apply(X1,X2))) )
| ~ spl22_153
| ~ spl22_280 ),
inference(resolution,[],[f2968,f1396]) ).
fof(f2968,plain,
( ! [X8,X7] :
( ~ in(X8,sK7(X7,X8))
| ~ empty(relation_dom(X7))
| sP0(X7,X8) )
| ~ spl22_280 ),
inference(avatar_component_clause,[],[f2967]) ).
fof(f27012,plain,
( spl22_1054
| ~ spl22_51
| ~ spl22_1022 ),
inference(avatar_split_clause,[],[f25142,f24069,f494,f27010]) ).
fof(f27010,plain,
( spl22_1054
<=> ! [X0] :
( ~ empty(set_intersection2(X0,relation_dom(sK5)))
| sP0(relation_dom_restriction(sK5,X0),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1054])]) ).
fof(f24069,plain,
( spl22_1022
<=> ! [X91] :
( ~ empty(set_intersection2(relation_dom(sK5),X91))
| sP0(relation_dom_restriction(sK5,X91),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1022])]) ).
fof(f25142,plain,
( ! [X0] :
( ~ empty(set_intersection2(X0,relation_dom(sK5)))
| sP0(relation_dom_restriction(sK5,X0),sK15) )
| ~ spl22_51
| ~ spl22_1022 ),
inference(superposition,[],[f24070,f495]) ).
fof(f24070,plain,
( ! [X91] :
( ~ empty(set_intersection2(relation_dom(sK5),X91))
| sP0(relation_dom_restriction(sK5,X91),sK15) )
| ~ spl22_1022 ),
inference(avatar_component_clause,[],[f24069]) ).
fof(f26658,plain,
( spl22_1053
| ~ spl22_114
| ~ spl22_906 ),
inference(avatar_split_clause,[],[f18494,f17763,f952,f26656]) ).
fof(f26656,plain,
( spl22_1053
<=> ! [X6] :
( ~ empty(relation_dom_restriction(sK5,X6))
| sK15 = set_intersection2(relation_dom(sK5),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1053])]) ).
fof(f18494,plain,
( ! [X6] :
( ~ empty(relation_dom_restriction(sK5,X6))
| sK15 = set_intersection2(relation_dom(sK5),X6) )
| ~ spl22_114
| ~ spl22_906 ),
inference(resolution,[],[f17764,f953]) ).
fof(f25742,plain,
( spl22_1052
| ~ spl22_124
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3902,f3857,f1103,f25740]) ).
fof(f25740,plain,
( spl22_1052
<=> ! [X20,X19] :
( sP0(X19,powerset(X20))
| ~ empty(X20)
| in(sK8(X19,powerset(X20)),relation_dom(X19))
| empty(sK7(X19,powerset(X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1052])]) ).
fof(f3902,plain,
( ! [X19,X20] :
( sP0(X19,powerset(X20))
| ~ empty(X20)
| in(sK8(X19,powerset(X20)),relation_dom(X19))
| empty(sK7(X19,powerset(X20))) )
| ~ spl22_124
| ~ spl22_350 ),
inference(resolution,[],[f3858,f1104]) ).
fof(f25738,plain,
( spl22_1051
| ~ spl22_197
| ~ spl22_349 ),
inference(avatar_split_clause,[],[f3894,f3853,f1926,f25736]) ).
fof(f25736,plain,
( spl22_1051
<=> ! [X0] :
( element(sK8(sK15,sK6(X0)),sK15)
| element(sK7(sK15,sK6(X0)),X0)
| sP0(sK15,sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1051])]) ).
fof(f3894,plain,
( ! [X0] :
( element(sK8(sK15,sK6(X0)),sK15)
| element(sK7(sK15,sK6(X0)),X0)
| sP0(sK15,sK6(X0))
| empty(X0) )
| ~ spl22_197
| ~ spl22_349 ),
inference(superposition,[],[f3854,f1928]) ).
fof(f25734,plain,
( spl22_1050
| ~ spl22_197
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3887,f3849,f1926,f25732]) ).
fof(f25732,plain,
( spl22_1050
<=> ! [X0] :
( in(sK8(sK15,sK6(X0)),sK15)
| element(sK7(sK15,sK6(X0)),X0)
| empty(X0)
| sP0(sK15,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1050])]) ).
fof(f3887,plain,
( ! [X0] :
( in(sK8(sK15,sK6(X0)),sK15)
| element(sK7(sK15,sK6(X0)),X0)
| empty(X0)
| sP0(sK15,sK6(X0)) )
| ~ spl22_197
| ~ spl22_348 ),
inference(superposition,[],[f3850,f1928]) ).
fof(f25730,plain,
( spl22_1049
| ~ spl22_52
| ~ spl22_337 ),
inference(avatar_split_clause,[],[f3737,f3449,f498,f25728]) ).
fof(f25728,plain,
( spl22_1049
<=> ! [X9,X8,X10] :
( sP2(powerset(X8),X9,sK10(powerset(X10)))
| ~ empty(X10)
| subset(sK13(powerset(X8),X9,sK10(powerset(X10))),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1049])]) ).
fof(f3737,plain,
( ! [X10,X8,X9] :
( sP2(powerset(X8),X9,sK10(powerset(X10)))
| ~ empty(X10)
| subset(sK13(powerset(X8),X9,sK10(powerset(X10))),X8) )
| ~ spl22_52
| ~ spl22_337 ),
inference(resolution,[],[f3450,f499]) ).
fof(f25726,plain,
( spl22_1048
| ~ spl22_52
| ~ spl22_335 ),
inference(avatar_split_clause,[],[f3732,f3441,f498,f25724]) ).
fof(f25724,plain,
( spl22_1048
<=> ! [X9,X8,X10] :
( sP2(sK10(powerset(X8)),X9,powerset(X10))
| ~ empty(X8)
| subset(sK13(sK10(powerset(X8)),X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1048])]) ).
fof(f3732,plain,
( ! [X10,X8,X9] :
( sP2(sK10(powerset(X8)),X9,powerset(X10))
| ~ empty(X8)
| subset(sK13(sK10(powerset(X8)),X9,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_335 ),
inference(resolution,[],[f3442,f499]) ).
fof(f25722,plain,
( spl22_1047
| ~ spl22_52
| ~ spl22_332 ),
inference(avatar_split_clause,[],[f3714,f3429,f498,f25720]) ).
fof(f25720,plain,
( spl22_1047
<=> ! [X9,X8,X10] :
( sP2(X8,powerset(X9),sK10(powerset(X10)))
| ~ empty(X10)
| subset(sK13(X8,powerset(X9),sK10(powerset(X10))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1047])]) ).
fof(f3714,plain,
( ! [X10,X8,X9] :
( sP2(X8,powerset(X9),sK10(powerset(X10)))
| ~ empty(X10)
| subset(sK13(X8,powerset(X9),sK10(powerset(X10))),X9) )
| ~ spl22_52
| ~ spl22_332 ),
inference(resolution,[],[f3430,f499]) ).
fof(f25718,plain,
( spl22_1046
| ~ spl22_52
| ~ spl22_330 ),
inference(avatar_split_clause,[],[f3709,f3421,f498,f25716]) ).
fof(f25716,plain,
( spl22_1046
<=> ! [X9,X8,X10] :
( sP2(X8,sK10(powerset(X9)),powerset(X10))
| ~ empty(X9)
| subset(sK13(X8,sK10(powerset(X9)),powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1046])]) ).
fof(f3709,plain,
( ! [X10,X8,X9] :
( sP2(X8,sK10(powerset(X9)),powerset(X10))
| ~ empty(X9)
| subset(sK13(X8,sK10(powerset(X9)),powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_330 ),
inference(resolution,[],[f3422,f499]) ).
fof(f25714,plain,
( spl22_1045
| ~ spl22_56
| ~ spl22_327 ),
inference(avatar_split_clause,[],[f3696,f3392,f540,f25712]) ).
fof(f25712,plain,
( spl22_1045
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1045])]) ).
fof(f3696,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X11,X12,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X11,X12,sK10(powerset(X13))),X13) )
| ~ spl22_56
| ~ spl22_327 ),
inference(resolution,[],[f3393,f541]) ).
fof(f25710,plain,
( spl22_1044
| ~ spl22_52
| ~ spl22_327 ),
inference(avatar_split_clause,[],[f3695,f3392,f498,f25708]) ).
fof(f25708,plain,
( spl22_1044
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1044])]) ).
fof(f3695,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X8,X9,sK10(powerset(powerset(X10))))
| subset(sK13(X8,X9,sK10(powerset(powerset(X10)))),X10) )
| ~ spl22_52
| ~ spl22_327 ),
inference(resolution,[],[f3393,f499]) ).
fof(f25706,plain,
( spl22_1043
| ~ spl22_56
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3687,f3384,f540,f25704]) ).
fof(f25704,plain,
( spl22_1043
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(sK10(powerset(X12)),X13,X11)
| empty(X12)
| in(sK13(sK10(powerset(X12)),X13,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1043])]) ).
fof(f3687,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(sK10(powerset(X12)),X13,X11)
| empty(X12)
| in(sK13(sK10(powerset(X12)),X13,X11),X12) )
| ~ spl22_56
| ~ spl22_325 ),
inference(resolution,[],[f3385,f541]) ).
fof(f25702,plain,
( spl22_1042
| ~ spl22_615
| ~ spl22_1023 ),
inference(avatar_split_clause,[],[f25442,f25336,f8735,f25700]) ).
fof(f8735,plain,
( spl22_615
<=> ! [X18,X17] :
( ~ sP0(X17,sK15)
| sP0(X17,X18)
| ~ empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_615])]) ).
fof(f25442,plain,
( ! [X0] :
( sP0(relation_dom_restriction(sK5,sK15),X0)
| ~ empty(X0) )
| ~ spl22_615
| ~ spl22_1023 ),
inference(resolution,[],[f25338,f8736]) ).
fof(f8736,plain,
( ! [X18,X17] :
( ~ sP0(X17,sK15)
| sP0(X17,X18)
| ~ empty(X18) )
| ~ spl22_615 ),
inference(avatar_component_clause,[],[f8735]) ).
fof(f25698,plain,
( spl22_1041
| ~ spl22_52
| ~ spl22_325 ),
inference(avatar_split_clause,[],[f3686,f3384,f498,f25696]) ).
fof(f25696,plain,
( spl22_1041
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(sK10(powerset(powerset(X9))),X10,X8)
| subset(sK13(sK10(powerset(powerset(X9))),X10,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1041])]) ).
fof(f3686,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(sK10(powerset(powerset(X9))),X10,X8)
| subset(sK13(sK10(powerset(powerset(X9))),X10,X8),X9) )
| ~ spl22_52
| ~ spl22_325 ),
inference(resolution,[],[f3385,f499]) ).
fof(f25694,plain,
( spl22_1040
| ~ spl22_56
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3678,f3376,f540,f25692]) ).
fof(f25692,plain,
( spl22_1040
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(X12,X11,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X12,X11,sK10(powerset(X13))),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1040])]) ).
fof(f3678,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X12,X11,sK10(powerset(X13)))
| empty(X13)
| in(sK13(X12,X11,sK10(powerset(X13))),X13) )
| ~ spl22_56
| ~ spl22_323 ),
inference(resolution,[],[f3377,f541]) ).
fof(f25690,plain,
( spl22_1039
| ~ spl22_52
| ~ spl22_323 ),
inference(avatar_split_clause,[],[f3677,f3376,f498,f25688]) ).
fof(f25688,plain,
( spl22_1039
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X9,X8,sK10(powerset(powerset(X10))))
| subset(sK13(X9,X8,sK10(powerset(powerset(X10)))),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1039])]) ).
fof(f3677,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X9,X8,sK10(powerset(powerset(X10))))
| subset(sK13(X9,X8,sK10(powerset(powerset(X10)))),X10) )
| ~ spl22_52
| ~ spl22_323 ),
inference(resolution,[],[f3377,f499]) ).
fof(f25686,plain,
( spl22_1038
| ~ spl22_56
| ~ spl22_321 ),
inference(avatar_split_clause,[],[f3661,f3368,f540,f25684]) ).
fof(f25684,plain,
( spl22_1038
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(X12,sK10(powerset(X13)),X11)
| empty(X13)
| in(sK13(X12,sK10(powerset(X13)),X11),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1038])]) ).
fof(f3661,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X12,sK10(powerset(X13)),X11)
| empty(X13)
| in(sK13(X12,sK10(powerset(X13)),X11),X13) )
| ~ spl22_56
| ~ spl22_321 ),
inference(resolution,[],[f3369,f541]) ).
fof(f25682,plain,
( spl22_1037
| ~ spl22_52
| ~ spl22_321 ),
inference(avatar_split_clause,[],[f3660,f3368,f498,f25680]) ).
fof(f25680,plain,
( spl22_1037
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X9,sK10(powerset(powerset(X10))),X8)
| subset(sK13(X9,sK10(powerset(powerset(X10))),X8),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1037])]) ).
fof(f3660,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X9,sK10(powerset(powerset(X10))),X8)
| subset(sK13(X9,sK10(powerset(powerset(X10))),X8),X10) )
| ~ spl22_52
| ~ spl22_321 ),
inference(resolution,[],[f3369,f499]) ).
fof(f25678,plain,
( spl22_1036
| ~ spl22_52
| ~ spl22_307 ),
inference(avatar_split_clause,[],[f3285,f3260,f498,f25676]) ).
fof(f25676,plain,
( spl22_1036
<=> ! [X6,X7] :
( ~ empty(relation_dom(X6))
| sP0(X6,sK6(powerset(X7)))
| empty(powerset(X7))
| subset(sK7(X6,sK6(powerset(X7))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1036])]) ).
fof(f3285,plain,
( ! [X6,X7] :
( ~ empty(relation_dom(X6))
| sP0(X6,sK6(powerset(X7)))
| empty(powerset(X7))
| subset(sK7(X6,sK6(powerset(X7))),X7) )
| ~ spl22_52
| ~ spl22_307 ),
inference(resolution,[],[f3261,f499]) ).
fof(f25674,plain,
( spl22_1035
| ~ spl22_255
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3139,f3027,f2711,f25672]) ).
fof(f25672,plain,
( spl22_1035
<=> ! [X102,X100,X101] :
( ~ sP0(X100,sK13(sK15,X101,apply(X100,X102)))
| ~ in(X102,relation_dom(X100))
| sP2(sK15,X101,apply(X100,X102)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1035])]) ).
fof(f3139,plain,
( ! [X101,X102,X100] :
( ~ sP0(X100,sK13(sK15,X101,apply(X100,X102)))
| ~ in(X102,relation_dom(X100))
| sP2(sK15,X101,apply(X100,X102)) )
| ~ spl22_255
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2712]) ).
fof(f25670,plain,
( spl22_1034
| ~ spl22_254
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3138,f3027,f2707,f25668]) ).
fof(f25668,plain,
( spl22_1034
<=> ! [X98,X97,X99] :
( ~ sP0(X97,sK13(X98,sK15,apply(X97,X99)))
| ~ in(X99,relation_dom(X97))
| sP2(X98,sK15,apply(X97,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1034])]) ).
fof(f3138,plain,
( ! [X98,X99,X97] :
( ~ sP0(X97,sK13(X98,sK15,apply(X97,X99)))
| ~ in(X99,relation_dom(X97))
| sP2(X98,sK15,apply(X97,X99)) )
| ~ spl22_254
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2708]) ).
fof(f25666,plain,
( spl22_1033
| ~ spl22_253
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3137,f3027,f2703,f25664]) ).
fof(f25664,plain,
( spl22_1033
<=> ! [X96,X94,X95] :
( ~ sP0(X94,sK13(X95,apply(X94,X96),sK15))
| ~ in(X96,relation_dom(X94))
| sP2(X95,apply(X94,X96),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1033])]) ).
fof(f3137,plain,
( ! [X96,X94,X95] :
( ~ sP0(X94,sK13(X95,apply(X94,X96),sK15))
| ~ in(X96,relation_dom(X94))
| sP2(X95,apply(X94,X96),sK15) )
| ~ spl22_253
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2704]) ).
fof(f25662,plain,
( spl22_1032
| ~ spl22_252
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3136,f3027,f2699,f25660]) ).
fof(f25660,plain,
( spl22_1032
<=> ! [X93,X92,X91] :
( ~ sP0(X91,sK13(apply(X91,X92),X93,sK15))
| ~ in(X92,relation_dom(X91))
| sP2(apply(X91,X92),X93,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1032])]) ).
fof(f3136,plain,
( ! [X91,X92,X93] :
( ~ sP0(X91,sK13(apply(X91,X92),X93,sK15))
| ~ in(X92,relation_dom(X91))
| sP2(apply(X91,X92),X93,sK15) )
| ~ spl22_252
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2700]) ).
fof(f25441,plain,
( spl22_1031
| ~ spl22_153
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3111,f3027,f1395,f25439]) ).
fof(f25439,plain,
( spl22_1031
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,apply(X1,X2))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,apply(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1031])]) ).
fof(f3111,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,apply(X1,X2))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,apply(X0,X3)) )
| ~ spl22_153
| ~ spl22_288 ),
inference(resolution,[],[f3028,f1396]) ).
fof(f25437,plain,
( spl22_1030
| ~ spl22_44
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2938,f2799,f444,f25435]) ).
fof(f25435,plain,
( spl22_1030
<=> ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| relation_dom_restriction(X4,X5) = relation_dom_restriction(relation_dom_restriction(X4,X5),relation_dom(relation_dom_restriction(X4,X5)))
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1030])]) ).
fof(f2938,plain,
( ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| relation_dom_restriction(X4,X5) = relation_dom_restriction(relation_dom_restriction(X4,X5),relation_dom(relation_dom_restriction(X4,X5)))
| ~ relation(X4) )
| ~ spl22_44
| ~ spl22_276 ),
inference(resolution,[],[f2800,f445]) ).
fof(f25433,plain,
( spl22_1029
| ~ spl22_146
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2526,f2439,f1316,f25431]) ).
fof(f25431,plain,
( spl22_1029
<=> ! [X89,X88,X90] :
( in(sK13(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)),X88)
| sP2(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1029])]) ).
fof(f2526,plain,
( ! [X90,X88,X89] :
( in(sK13(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)),X88)
| sP2(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)) )
| ~ spl22_146
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1317]) ).
fof(f25429,plain,
( spl22_1028
| ~ spl22_145
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2525,f2439,f1312,f25427]) ).
fof(f25427,plain,
( spl22_1028
<=> ! [X86,X85,X87] :
( in(sK13(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)),X86)
| sP2(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1028])]) ).
fof(f2525,plain,
( ! [X86,X87,X85] :
( in(sK13(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)),X86)
| sP2(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)) )
| ~ spl22_145
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1313]) ).
fof(f25425,plain,
( spl22_1027
| ~ spl22_146
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2495,f2435,f1316,f25423]) ).
fof(f25423,plain,
( spl22_1027
<=> ! [X89,X88,X90] :
( in(sK13(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)),X89)
| sP2(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1027])]) ).
fof(f2495,plain,
( ! [X90,X88,X89] :
( in(sK13(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)),X89)
| sP2(set_intersection2(X88,X89),X90,set_intersection2(X88,X89)) )
| ~ spl22_146
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1317]) ).
fof(f25421,plain,
( spl22_1026
| ~ spl22_145
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2494,f2435,f1312,f25419]) ).
fof(f25419,plain,
( spl22_1026
<=> ! [X86,X85,X87] :
( in(sK13(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)),X87)
| sP2(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1026])]) ).
fof(f2494,plain,
( ! [X86,X87,X85] :
( in(sK13(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)),X87)
| sP2(X85,set_intersection2(X86,X87),set_intersection2(X86,X87)) )
| ~ spl22_145
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1313]) ).
fof(f25417,plain,
( spl22_1025
| ~ spl22_79
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2408,f2331,f718,f25415]) ).
fof(f25415,plain,
( spl22_1025
<=> ! [X9,X10] :
( ~ sP0(X9,sK15)
| sK7(X10,relation_dom(X9)) = apply(X10,sK8(X10,relation_dom(X9)))
| sP0(X10,relation_dom(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1025])]) ).
fof(f2408,plain,
( ! [X10,X9] :
( ~ sP0(X9,sK15)
| sK7(X10,relation_dom(X9)) = apply(X10,sK8(X10,relation_dom(X9)))
| sP0(X10,relation_dom(X9)) )
| ~ spl22_79
| ~ spl22_236 ),
inference(resolution,[],[f2332,f719]) ).
fof(f25406,plain,
( ~ spl22_91
| ~ spl22_42
| spl22_1024
| ~ spl22_179
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1971,f1926,f1671,f25404,f433,f795]) ).
fof(f25404,plain,
( spl22_1024
<=> ! [X10] :
( sK15 = relation_dom_restriction(X10,sK15)
| ~ relation(X10)
| ~ function(X10)
| in(sK12(sK15,X10),sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1024])]) ).
fof(f1671,plain,
( spl22_179
<=> ! [X0,X1] :
( relation_dom_restriction(X0,sK15) = X1
| relation_dom(X1) != sK15
| in(sK12(X1,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_179])]) ).
fof(f1971,plain,
( ! [X10] :
( sK15 = relation_dom_restriction(X10,sK15)
| in(sK12(sK15,X10),sK15)
| ~ function(X10)
| ~ relation(X10)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_179
| ~ spl22_197 ),
inference(trivial_inequality_removal,[],[f1967]) ).
fof(f1967,plain,
( ! [X10] :
( sK15 != sK15
| sK15 = relation_dom_restriction(X10,sK15)
| in(sK12(sK15,X10),sK15)
| ~ function(X10)
| ~ relation(X10)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_179
| ~ spl22_197 ),
inference(superposition,[],[f1672,f1928]) ).
fof(f1672,plain,
( ! [X0,X1] :
( relation_dom(X1) != sK15
| relation_dom_restriction(X0,sK15) = X1
| in(sK12(X1,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_179 ),
inference(avatar_component_clause,[],[f1671]) ).
fof(f25339,plain,
( ~ spl22_10
| spl22_1023
| ~ spl22_31
| ~ spl22_94
| ~ spl22_1022 ),
inference(avatar_split_clause,[],[f25147,f24069,f812,f373,f25336,f264]) ).
fof(f373,plain,
( spl22_31
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_31])]) ).
fof(f25147,plain,
( sP0(relation_dom_restriction(sK5,sK15),sK15)
| ~ empty(sK15)
| ~ spl22_31
| ~ spl22_94
| ~ spl22_1022 ),
inference(forward_demodulation,[],[f25146,f814]) ).
fof(f25146,plain,
( ~ empty(sK15)
| sP0(relation_dom_restriction(sK5,empty_set),sK15)
| ~ spl22_31
| ~ spl22_94
| ~ spl22_1022 ),
inference(forward_demodulation,[],[f25144,f814]) ).
fof(f25144,plain,
( ~ empty(empty_set)
| sP0(relation_dom_restriction(sK5,empty_set),sK15)
| ~ spl22_31
| ~ spl22_1022 ),
inference(superposition,[],[f24070,f374]) ).
fof(f374,plain,
( ! [X0] : empty_set = set_intersection2(X0,empty_set)
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f24071,plain,
( spl22_1022
| ~ spl22_219
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15092,f15007,f2148,f24069]) ).
fof(f2148,plain,
( spl22_219
<=> ! [X15] :
( sP0(X15,sK15)
| ~ empty(relation_dom(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_219])]) ).
fof(f15092,plain,
( ! [X91] :
( ~ empty(set_intersection2(relation_dom(sK5),X91))
| sP0(relation_dom_restriction(sK5,X91),sK15) )
| ~ spl22_219
| ~ spl22_823 ),
inference(superposition,[],[f2149,f15008]) ).
fof(f2149,plain,
( ! [X15] :
( ~ empty(relation_dom(X15))
| sP0(X15,sK15) )
| ~ spl22_219 ),
inference(avatar_component_clause,[],[f2148]) ).
fof(f23808,plain,
( spl22_1021
| ~ spl22_116
| ~ spl22_401 ),
inference(avatar_split_clause,[],[f5181,f5153,f959,f23806]) ).
fof(f23806,plain,
( spl22_1021
<=> ! [X75] :
( sP0(X75,sK15)
| apply(relation_dom_restriction(sK15,relation_dom(X75)),sK8(X75,sK15)) = apply(sK15,sK8(X75,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1021])]) ).
fof(f5181,plain,
( ! [X75] :
( sP0(X75,sK15)
| apply(relation_dom_restriction(sK15,relation_dom(X75)),sK8(X75,sK15)) = apply(sK15,sK8(X75,sK15)) )
| ~ spl22_116
| ~ spl22_401 ),
inference(resolution,[],[f5154,f960]) ).
fof(f23804,plain,
( spl22_1020
| ~ spl22_116
| ~ spl22_400 ),
inference(avatar_split_clause,[],[f5151,f5123,f959,f23802]) ).
fof(f23802,plain,
( spl22_1020
<=> ! [X75] :
( sP0(X75,sK15)
| apply(relation_dom_restriction(sK20,relation_dom(X75)),sK8(X75,sK15)) = apply(sK20,sK8(X75,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1020])]) ).
fof(f5151,plain,
( ! [X75] :
( sP0(X75,sK15)
| apply(relation_dom_restriction(sK20,relation_dom(X75)),sK8(X75,sK15)) = apply(sK20,sK8(X75,sK15)) )
| ~ spl22_116
| ~ spl22_400 ),
inference(resolution,[],[f5124,f960]) ).
fof(f23800,plain,
( spl22_1019
| ~ spl22_116
| ~ spl22_399 ),
inference(avatar_split_clause,[],[f5121,f5093,f959,f23798]) ).
fof(f23798,plain,
( spl22_1019
<=> ! [X75] :
( sP0(X75,sK15)
| apply(relation_dom_restriction(sK19,relation_dom(X75)),sK8(X75,sK15)) = apply(sK19,sK8(X75,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1019])]) ).
fof(f5121,plain,
( ! [X75] :
( sP0(X75,sK15)
| apply(relation_dom_restriction(sK19,relation_dom(X75)),sK8(X75,sK15)) = apply(sK19,sK8(X75,sK15)) )
| ~ spl22_116
| ~ spl22_399 ),
inference(resolution,[],[f5094,f960]) ).
fof(f23791,plain,
( spl22_1018
| ~ spl22_27
| ~ spl22_358 ),
inference(avatar_split_clause,[],[f4066,f4031,f347,f23789]) ).
fof(f23789,plain,
( spl22_1018
<=> ! [X0,X1] :
( empty(powerset(X0))
| apply(X1,X0) = apply(relation_dom_restriction(X1,powerset(X0)),X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1018])]) ).
fof(f347,plain,
( spl22_27
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_27])]) ).
fof(f4031,plain,
( spl22_358
<=> ! [X2,X4,X3] :
( empty(powerset(X2))
| ~ subset(X3,X2)
| apply(relation_dom_restriction(X4,powerset(X2)),X3) = apply(X4,X3)
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_358])]) ).
fof(f4066,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| apply(X1,X0) = apply(relation_dom_restriction(X1,powerset(X0)),X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_27
| ~ spl22_358 ),
inference(resolution,[],[f4032,f348]) ).
fof(f348,plain,
( ! [X0] : subset(X0,X0)
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f4032,plain,
( ! [X2,X3,X4] :
( ~ subset(X3,X2)
| empty(powerset(X2))
| apply(relation_dom_restriction(X4,powerset(X2)),X3) = apply(X4,X3)
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_358 ),
inference(avatar_component_clause,[],[f4031]) ).
fof(f23787,plain,
( spl22_1017
| ~ spl22_250
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4055,f4027,f2571,f23785]) ).
fof(f23785,plain,
( spl22_1017
<=> ! [X4,X5,X3] :
( element(sK7(X3,sK10(powerset(X4))),X4)
| sP0(X3,sK10(powerset(X4)))
| ~ sP0(X3,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1017])]) ).
fof(f4055,plain,
( ! [X3,X4,X5] :
( element(sK7(X3,sK10(powerset(X4))),X4)
| sP0(X3,sK10(powerset(X4)))
| ~ sP0(X3,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_357 ),
inference(resolution,[],[f4028,f2572]) ).
fof(f23783,plain,
( spl22_1016
| ~ spl22_236
| ~ spl22_354 ),
inference(avatar_split_clause,[],[f4013,f3873,f2331,f23781]) ).
fof(f23781,plain,
( spl22_1016
<=> ! [X38,X36,X37] :
( subset(sK13(powerset(X36),X37,relation_dom(X38)),X36)
| sP2(powerset(X36),X37,relation_dom(X38))
| ~ sP0(X38,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1016])]) ).
fof(f4013,plain,
( ! [X38,X36,X37] :
( subset(sK13(powerset(X36),X37,relation_dom(X38)),X36)
| sP2(powerset(X36),X37,relation_dom(X38))
| ~ sP0(X38,sK15) )
| ~ spl22_236
| ~ spl22_354 ),
inference(resolution,[],[f3874,f2332]) ).
fof(f23779,plain,
( spl22_1015
| ~ spl22_236
| ~ spl22_353 ),
inference(avatar_split_clause,[],[f3991,f3869,f2331,f23777]) ).
fof(f23777,plain,
( spl22_1015
<=> ! [X36,X37,X35] :
( subset(sK13(relation_dom(X35),X36,powerset(X37)),X37)
| sP2(relation_dom(X35),X36,powerset(X37))
| ~ sP0(X35,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1015])]) ).
fof(f3991,plain,
( ! [X36,X37,X35] :
( subset(sK13(relation_dom(X35),X36,powerset(X37)),X37)
| sP2(relation_dom(X35),X36,powerset(X37))
| ~ sP0(X35,sK15) )
| ~ spl22_236
| ~ spl22_353 ),
inference(resolution,[],[f3870,f2332]) ).
fof(f23775,plain,
( spl22_1014
| ~ spl22_236
| ~ spl22_352 ),
inference(avatar_split_clause,[],[f3969,f3865,f2331,f23773]) ).
fof(f23773,plain,
( spl22_1014
<=> ! [X38,X36,X37] :
( subset(sK13(X36,powerset(X37),relation_dom(X38)),X37)
| sP2(X36,powerset(X37),relation_dom(X38))
| ~ sP0(X38,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1014])]) ).
fof(f3969,plain,
( ! [X38,X36,X37] :
( subset(sK13(X36,powerset(X37),relation_dom(X38)),X37)
| sP2(X36,powerset(X37),relation_dom(X38))
| ~ sP0(X38,sK15) )
| ~ spl22_236
| ~ spl22_352 ),
inference(resolution,[],[f3866,f2332]) ).
fof(f23771,plain,
( spl22_1013
| ~ spl22_236
| ~ spl22_351 ),
inference(avatar_split_clause,[],[f3947,f3861,f2331,f23769]) ).
fof(f23769,plain,
( spl22_1013
<=> ! [X38,X36,X37] :
( subset(sK13(X36,relation_dom(X37),powerset(X38)),X38)
| sP2(X36,relation_dom(X37),powerset(X38))
| ~ sP0(X37,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1013])]) ).
fof(f3947,plain,
( ! [X38,X36,X37] :
( subset(sK13(X36,relation_dom(X37),powerset(X38)),X38)
| sP2(X36,relation_dom(X37),powerset(X38))
| ~ sP0(X37,sK15) )
| ~ spl22_236
| ~ spl22_351 ),
inference(resolution,[],[f3862,f2332]) ).
fof(f23767,plain,
( spl22_1012
| ~ spl22_250
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3877,f3849,f2571,f23765]) ).
fof(f23765,plain,
( spl22_1012
<=> ! [X4,X5,X3] :
( element(sK7(X3,sK6(X4)),X4)
| empty(X4)
| sP0(X3,sK6(X4))
| ~ sP0(X3,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1012])]) ).
fof(f3877,plain,
( ! [X3,X4,X5] :
( element(sK7(X3,sK6(X4)),X4)
| empty(X4)
| sP0(X3,sK6(X4))
| ~ sP0(X3,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_348 ),
inference(resolution,[],[f3850,f2572]) ).
fof(f23763,plain,
( spl22_1011
| ~ spl22_45
| ~ spl22_343 ),
inference(avatar_split_clause,[],[f3810,f3754,f448,f23761]) ).
fof(f23761,plain,
( spl22_1011
<=> ! [X16,X15] :
( subset(sK7(X15,powerset(X16)),X16)
| sP0(X15,powerset(X16))
| ~ in(relation_dom(X15),sK8(X15,powerset(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1011])]) ).
fof(f3754,plain,
( spl22_343
<=> ! [X6,X7] :
( in(sK8(X6,powerset(X7)),relation_dom(X6))
| sP0(X6,powerset(X7))
| subset(sK7(X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_343])]) ).
fof(f3810,plain,
( ! [X16,X15] :
( subset(sK7(X15,powerset(X16)),X16)
| sP0(X15,powerset(X16))
| ~ in(relation_dom(X15),sK8(X15,powerset(X16))) )
| ~ spl22_45
| ~ spl22_343 ),
inference(resolution,[],[f3755,f449]) ).
fof(f3755,plain,
( ! [X6,X7] :
( in(sK8(X6,powerset(X7)),relation_dom(X6))
| subset(sK7(X6,powerset(X7)),X7)
| sP0(X6,powerset(X7)) )
| ~ spl22_343 ),
inference(avatar_component_clause,[],[f3754]) ).
fof(f23759,plain,
( spl22_1010
| ~ spl22_52
| ~ spl22_309 ),
inference(avatar_split_clause,[],[f3298,f3268,f498,f23757]) ).
fof(f23757,plain,
( spl22_1010
<=> ! [X9,X8,X10] :
( ~ sP0(X8,sK6(powerset(X9)))
| ~ in(X10,relation_dom(X8))
| empty(powerset(X9))
| subset(apply(X8,X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1010])]) ).
fof(f3298,plain,
( ! [X10,X8,X9] :
( ~ sP0(X8,sK6(powerset(X9)))
| ~ in(X10,relation_dom(X8))
| empty(powerset(X9))
| subset(apply(X8,X10),X9) )
| ~ spl22_52
| ~ spl22_309 ),
inference(resolution,[],[f3269,f499]) ).
fof(f23755,plain,
( spl22_1009
| ~ spl22_56
| ~ spl22_308 ),
inference(avatar_split_clause,[],[f3291,f3264,f540,f23753]) ).
fof(f23753,plain,
( spl22_1009
<=> ! [X9,X8] :
( ~ empty(relation_dom(X8))
| sP0(X8,sK10(powerset(X9)))
| empty(X9)
| in(sK7(X8,sK10(powerset(X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1009])]) ).
fof(f3291,plain,
( ! [X8,X9] :
( ~ empty(relation_dom(X8))
| sP0(X8,sK10(powerset(X9)))
| empty(X9)
| in(sK7(X8,sK10(powerset(X9))),X9) )
| ~ spl22_56
| ~ spl22_308 ),
inference(resolution,[],[f3265,f541]) ).
fof(f23743,plain,
( spl22_1008
| ~ spl22_52
| ~ spl22_308 ),
inference(avatar_split_clause,[],[f3290,f3264,f498,f23741]) ).
fof(f23741,plain,
( spl22_1008
<=> ! [X6,X7] :
( ~ empty(relation_dom(X6))
| sP0(X6,sK10(powerset(powerset(X7))))
| subset(sK7(X6,sK10(powerset(powerset(X7)))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1008])]) ).
fof(f3290,plain,
( ! [X6,X7] :
( ~ empty(relation_dom(X6))
| sP0(X6,sK10(powerset(powerset(X7))))
| subset(sK7(X6,sK10(powerset(powerset(X7)))),X7) )
| ~ spl22_52
| ~ spl22_308 ),
inference(resolution,[],[f3265,f499]) ).
fof(f23739,plain,
( spl22_1007
| ~ spl22_52
| ~ spl22_302 ),
inference(avatar_split_clause,[],[f3246,f3229,f498,f23737]) ).
fof(f23737,plain,
( spl22_1007
<=> ! [X6,X7] :
( element(sK8(X6,powerset(X7)),relation_dom(X6))
| sP0(X6,powerset(X7))
| subset(sK7(X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1007])]) ).
fof(f3246,plain,
( ! [X6,X7] :
( element(sK8(X6,powerset(X7)),relation_dom(X6))
| sP0(X6,powerset(X7))
| subset(sK7(X6,powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_302 ),
inference(resolution,[],[f3230,f499]) ).
fof(f23735,plain,
( spl22_1006
| ~ spl22_67
| ~ spl22_295 ),
inference(avatar_split_clause,[],[f3167,f3067,f633,f23733]) ).
fof(f23733,plain,
( spl22_1006
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1006])]) ).
fof(f3067,plain,
( spl22_295
<=> ! [X11,X12,X10] :
( sP2(X10,X11,X12)
| ~ empty(X10)
| element(sK13(X10,X11,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_295])]) ).
fof(f3167,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) )
| ~ spl22_67
| ~ spl22_295 ),
inference(resolution,[],[f3068,f634]) ).
fof(f3068,plain,
( ! [X10,X11,X12] :
( element(sK13(X10,X11,X12),X12)
| ~ empty(X10)
| sP2(X10,X11,X12) )
| ~ spl22_295 ),
inference(avatar_component_clause,[],[f3067]) ).
fof(f23731,plain,
( spl22_1005
| ~ spl22_67
| ~ spl22_293 ),
inference(avatar_split_clause,[],[f3162,f3059,f633,f23729]) ).
fof(f23729,plain,
( spl22_1005
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(powerset(X5),X6,X4)
| element(X7,X5)
| ~ in(X7,sK13(powerset(X5),X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1005])]) ).
fof(f3059,plain,
( spl22_293
<=> ! [X9,X11,X10] :
( sP2(X9,X10,X11)
| ~ empty(X11)
| element(sK13(X9,X10,X11),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_293])]) ).
fof(f3162,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(powerset(X5),X6,X4)
| element(X7,X5)
| ~ in(X7,sK13(powerset(X5),X6,X4)) )
| ~ spl22_67
| ~ spl22_293 ),
inference(resolution,[],[f3060,f634]) ).
fof(f3060,plain,
( ! [X10,X11,X9] :
( element(sK13(X9,X10,X11),X9)
| ~ empty(X11)
| sP2(X9,X10,X11) )
| ~ spl22_293 ),
inference(avatar_component_clause,[],[f3059]) ).
fof(f23727,plain,
( spl22_1004
| ~ spl22_67
| ~ spl22_291 ),
inference(avatar_split_clause,[],[f3157,f3051,f633,f23725]) ).
fof(f23725,plain,
( spl22_1004
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X5,X4,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X5,X4,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1004])]) ).
fof(f3051,plain,
( spl22_291
<=> ! [X11,X12,X10] :
( sP2(X10,X11,X12)
| ~ empty(X11)
| element(sK13(X10,X11,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_291])]) ).
fof(f3157,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X5,X4,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X5,X4,powerset(X6))) )
| ~ spl22_67
| ~ spl22_291 ),
inference(resolution,[],[f3052,f634]) ).
fof(f3052,plain,
( ! [X10,X11,X12] :
( element(sK13(X10,X11,X12),X12)
| ~ empty(X11)
| sP2(X10,X11,X12) )
| ~ spl22_291 ),
inference(avatar_component_clause,[],[f3051]) ).
fof(f23723,plain,
( spl22_1003
| ~ spl22_67
| ~ spl22_289 ),
inference(avatar_split_clause,[],[f3152,f3031,f633,f23721]) ).
fof(f23721,plain,
( spl22_1003
<=> ! [X5,X4,X7,X6] :
( ~ empty(X4)
| sP2(X5,powerset(X6),X4)
| element(X7,X6)
| ~ in(X7,sK13(X5,powerset(X6),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1003])]) ).
fof(f3031,plain,
( spl22_289
<=> ! [X9,X11,X10] :
( sP2(X9,X10,X11)
| ~ empty(X11)
| element(sK13(X9,X10,X11),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_289])]) ).
fof(f3152,plain,
( ! [X6,X7,X4,X5] :
( ~ empty(X4)
| sP2(X5,powerset(X6),X4)
| element(X7,X6)
| ~ in(X7,sK13(X5,powerset(X6),X4)) )
| ~ spl22_67
| ~ spl22_289 ),
inference(resolution,[],[f3032,f634]) ).
fof(f3032,plain,
( ! [X10,X11,X9] :
( element(sK13(X9,X10,X11),X10)
| ~ empty(X11)
| sP2(X9,X10,X11) )
| ~ spl22_289 ),
inference(avatar_component_clause,[],[f3031]) ).
fof(f23719,plain,
( spl22_1002
| ~ spl22_67
| ~ spl22_264 ),
inference(avatar_split_clause,[],[f2887,f2747,f633,f23717]) ).
fof(f23717,plain,
( spl22_1002
<=> ! [X4,X5,X3] :
( sP2(powerset(X3),X4,powerset(X3))
| element(X5,X3)
| ~ in(X5,sK13(powerset(X3),X4,powerset(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1002])]) ).
fof(f2747,plain,
( spl22_264
<=> ! [X7,X8] :
( sP2(X7,X8,X7)
| element(sK13(X7,X8,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_264])]) ).
fof(f2887,plain,
( ! [X3,X4,X5] :
( sP2(powerset(X3),X4,powerset(X3))
| element(X5,X3)
| ~ in(X5,sK13(powerset(X3),X4,powerset(X3))) )
| ~ spl22_67
| ~ spl22_264 ),
inference(resolution,[],[f2748,f634]) ).
fof(f2748,plain,
( ! [X8,X7] :
( element(sK13(X7,X8,X7),X7)
| sP2(X7,X8,X7) )
| ~ spl22_264 ),
inference(avatar_component_clause,[],[f2747]) ).
fof(f23715,plain,
( spl22_1001
| ~ spl22_67
| ~ spl22_261 ),
inference(avatar_split_clause,[],[f2878,f2735,f633,f23713]) ).
fof(f23713,plain,
( spl22_1001
<=> ! [X4,X5,X3] :
( sP2(X3,powerset(X4),powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(X3,powerset(X4),powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1001])]) ).
fof(f2735,plain,
( spl22_261
<=> ! [X8,X7] :
( sP2(X7,X8,X8)
| element(sK13(X7,X8,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_261])]) ).
fof(f2878,plain,
( ! [X3,X4,X5] :
( sP2(X3,powerset(X4),powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(X3,powerset(X4),powerset(X4))) )
| ~ spl22_67
| ~ spl22_261 ),
inference(resolution,[],[f2736,f634]) ).
fof(f2736,plain,
( ! [X8,X7] :
( element(sK13(X7,X8,X8),X8)
| sP2(X7,X8,X8) )
| ~ spl22_261 ),
inference(avatar_component_clause,[],[f2735]) ).
fof(f23711,plain,
( spl22_1000
| ~ spl22_78
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2694,f2571,f692,f23709]) ).
fof(f23709,plain,
( spl22_1000
<=> ! [X95,X97,X94,X96] :
( ~ sP0(X94,X95)
| ~ empty(X95)
| in(sK13(relation_dom(X94),X96,X97),X97)
| sP2(relation_dom(X94),X96,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1000])]) ).
fof(f2694,plain,
( ! [X96,X94,X97,X95] :
( ~ sP0(X94,X95)
| ~ empty(X95)
| in(sK13(relation_dom(X94),X96,X97),X97)
| sP2(relation_dom(X94),X96,X97) )
| ~ spl22_78
| ~ spl22_250 ),
inference(resolution,[],[f2572,f693]) ).
fof(f23707,plain,
( spl22_999
| ~ spl22_170
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2692,f2571,f1550,f23705]) ).
fof(f23705,plain,
( spl22_999
<=> ! [X88,X87,X89,X86] :
( ~ sP0(X86,X87)
| ~ empty(X87)
| element(sK13(relation_dom(X86),X88,X89),X89)
| sP2(relation_dom(X86),X88,X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_999])]) ).
fof(f2692,plain,
( ! [X88,X86,X89,X87] :
( ~ sP0(X86,X87)
| ~ empty(X87)
| element(sK13(relation_dom(X86),X88,X89),X89)
| sP2(relation_dom(X86),X88,X89) )
| ~ spl22_170
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1551]) ).
fof(f23687,plain,
( spl22_998
| ~ spl22_77
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2690,f2571,f688,f23685]) ).
fof(f23685,plain,
( spl22_998
<=> ! [X81,X78,X80,X79] :
( ~ sP0(X78,X79)
| ~ empty(X79)
| in(sK13(X80,relation_dom(X78),X81),X81)
| sP2(X80,relation_dom(X78),X81) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_998])]) ).
fof(f2690,plain,
( ! [X80,X78,X81,X79] :
( ~ sP0(X78,X79)
| ~ empty(X79)
| in(sK13(X80,relation_dom(X78),X81),X81)
| sP2(X80,relation_dom(X78),X81) )
| ~ spl22_77
| ~ spl22_250 ),
inference(resolution,[],[f2572,f689]) ).
fof(f23683,plain,
( spl22_997
| ~ spl22_166
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2688,f2571,f1533,f23681]) ).
fof(f23681,plain,
( spl22_997
<=> ! [X73,X71,X70,X72] :
( ~ sP0(X70,X71)
| ~ empty(X71)
| element(sK13(X72,relation_dom(X70),X73),X73)
| sP2(X72,relation_dom(X70),X73) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_997])]) ).
fof(f2688,plain,
( ! [X72,X70,X73,X71] :
( ~ sP0(X70,X71)
| ~ empty(X71)
| element(sK13(X72,relation_dom(X70),X73),X73)
| sP2(X72,relation_dom(X70),X73) )
| ~ spl22_166
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1534]) ).
fof(f23679,plain,
( spl22_996
| ~ spl22_172
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2684,f2571,f1558,f23677]) ).
fof(f23677,plain,
( spl22_996
<=> ! [X55,X54,X56,X57] :
( ~ sP0(X54,X55)
| ~ empty(X55)
| element(sK13(X56,X57,relation_dom(X54)),X56)
| sP2(X56,X57,relation_dom(X54)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_996])]) ).
fof(f2684,plain,
( ! [X56,X54,X57,X55] :
( ~ sP0(X54,X55)
| ~ empty(X55)
| element(sK13(X56,X57,relation_dom(X54)),X56)
| sP2(X56,X57,relation_dom(X54)) )
| ~ spl22_172
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1559]) ).
fof(f23675,plain,
( spl22_995
| ~ spl22_168
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2683,f2571,f1542,f23673]) ).
fof(f23673,plain,
( spl22_995
<=> ! [X51,X53,X50,X52] :
( ~ sP0(X50,X51)
| ~ empty(X51)
| element(sK13(X52,X53,relation_dom(X50)),X53)
| sP2(X52,X53,relation_dom(X50)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_995])]) ).
fof(f2683,plain,
( ! [X50,X51,X52,X53] :
( ~ sP0(X50,X51)
| ~ empty(X51)
| element(sK13(X52,X53,relation_dom(X50)),X53)
| sP2(X52,X53,relation_dom(X50)) )
| ~ spl22_168
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1543]) ).
fof(f23671,plain,
( spl22_994
| ~ spl22_78
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2680,f2571,f692,f23669]) ).
fof(f23669,plain,
( spl22_994
<=> ! [X38,X41,X40,X39] :
( ~ sP0(X38,X39)
| ~ empty(X39)
| in(sK13(X40,X41,relation_dom(X38)),X40)
| sP2(X40,X41,relation_dom(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_994])]) ).
fof(f2680,plain,
( ! [X40,X38,X41,X39] :
( ~ sP0(X38,X39)
| ~ empty(X39)
| in(sK13(X40,X41,relation_dom(X38)),X40)
| sP2(X40,X41,relation_dom(X38)) )
| ~ spl22_78
| ~ spl22_250 ),
inference(resolution,[],[f2572,f693]) ).
fof(f23667,plain,
( spl22_993
| ~ spl22_77
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2679,f2571,f688,f23665]) ).
fof(f23665,plain,
( spl22_993
<=> ! [X37,X34,X36,X35] :
( ~ sP0(X34,X35)
| ~ empty(X35)
| in(sK13(X36,X37,relation_dom(X34)),X37)
| sP2(X36,X37,relation_dom(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_993])]) ).
fof(f2679,plain,
( ! [X36,X37,X34,X35] :
( ~ sP0(X34,X35)
| ~ empty(X35)
| in(sK13(X36,X37,relation_dom(X34)),X37)
| sP2(X36,X37,relation_dom(X34)) )
| ~ spl22_77
| ~ spl22_250 ),
inference(resolution,[],[f2572,f689]) ).
fof(f23657,plain,
( spl22_992
| ~ spl22_230
| ~ spl22_462 ),
inference(avatar_split_clause,[],[f6455,f6425,f2286,f23655]) ).
fof(f23655,plain,
( spl22_992
<=> ! [X13,X14,X12,X15] :
( ~ function(X12)
| ~ relation(X12)
| ~ function(relation_dom_restriction(X12,X13))
| ~ relation(relation_dom_restriction(X12,X13))
| ~ in(X14,relation_dom(X15))
| apply(relation_dom_restriction(X12,X13),apply(X15,X14)) = apply(X12,apply(X15,X14))
| sK7(X15,relation_dom(relation_dom_restriction(X12,X13))) = apply(X15,sK8(X15,relation_dom(relation_dom_restriction(X12,X13))))
| apply(relation_dom_restriction(sK5,relation_dom(relation_dom_restriction(X12,X13))),sK7(X15,relation_dom(relation_dom_restriction(X12,X13)))) = apply(sK5,sK7(X15,relation_dom(relation_dom_restriction(X12,X13)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_992])]) ).
fof(f2286,plain,
( spl22_230
<=> ! [X16,X17] :
( sP0(X16,X17)
| sK7(X16,X17) = apply(X16,sK8(X16,X17))
| apply(relation_dom_restriction(sK5,X17),sK7(X16,X17)) = apply(sK5,sK7(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_230])]) ).
fof(f6425,plain,
( spl22_462
<=> ! [X0,X3,X2,X1] :
( apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,relation_dom(relation_dom_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_462])]) ).
fof(f6455,plain,
( ! [X14,X15,X12,X13] :
( ~ function(X12)
| ~ relation(X12)
| ~ function(relation_dom_restriction(X12,X13))
| ~ relation(relation_dom_restriction(X12,X13))
| ~ in(X14,relation_dom(X15))
| apply(relation_dom_restriction(X12,X13),apply(X15,X14)) = apply(X12,apply(X15,X14))
| sK7(X15,relation_dom(relation_dom_restriction(X12,X13))) = apply(X15,sK8(X15,relation_dom(relation_dom_restriction(X12,X13))))
| apply(relation_dom_restriction(sK5,relation_dom(relation_dom_restriction(X12,X13))),sK7(X15,relation_dom(relation_dom_restriction(X12,X13)))) = apply(sK5,sK7(X15,relation_dom(relation_dom_restriction(X12,X13)))) )
| ~ spl22_230
| ~ spl22_462 ),
inference(resolution,[],[f6426,f2287]) ).
fof(f2287,plain,
( ! [X16,X17] :
( sP0(X16,X17)
| sK7(X16,X17) = apply(X16,sK8(X16,X17))
| apply(relation_dom_restriction(sK5,X17),sK7(X16,X17)) = apply(sK5,sK7(X16,X17)) )
| ~ spl22_230 ),
inference(avatar_component_clause,[],[f2286]) ).
fof(f6426,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X3,relation_dom(X2))
| apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3)) )
| ~ spl22_462 ),
inference(avatar_component_clause,[],[f6425]) ).
fof(f23207,plain,
( spl22_991
| ~ spl22_230
| ~ spl22_417 ),
inference(avatar_split_clause,[],[f5552,f5478,f2286,f23205]) ).
fof(f23205,plain,
( spl22_991
<=> ! [X0,X3,X2,X1] :
( in(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| sP2(apply(X0,X1),X2,X3)
| sK7(X0,sK13(apply(X0,X1),X2,X3)) = apply(X0,sK8(X0,sK13(apply(X0,X1),X2,X3)))
| apply(relation_dom_restriction(sK5,sK13(apply(X0,X1),X2,X3)),sK7(X0,sK13(apply(X0,X1),X2,X3))) = apply(sK5,sK7(X0,sK13(apply(X0,X1),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_991])]) ).
fof(f5478,plain,
( spl22_417
<=> ! [X0,X3,X2,X1] :
( sP2(apply(X0,X1),X2,X3)
| in(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_417])]) ).
fof(f5552,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| sP2(apply(X0,X1),X2,X3)
| sK7(X0,sK13(apply(X0,X1),X2,X3)) = apply(X0,sK8(X0,sK13(apply(X0,X1),X2,X3)))
| apply(relation_dom_restriction(sK5,sK13(apply(X0,X1),X2,X3)),sK7(X0,sK13(apply(X0,X1),X2,X3))) = apply(sK5,sK7(X0,sK13(apply(X0,X1),X2,X3))) )
| ~ spl22_230
| ~ spl22_417 ),
inference(resolution,[],[f5479,f2287]) ).
fof(f5479,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,sK13(apply(X0,X1),X2,X3))
| in(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| sP2(apply(X0,X1),X2,X3) )
| ~ spl22_417 ),
inference(avatar_component_clause,[],[f5478]) ).
fof(f23203,plain,
( spl22_990
| ~ spl22_230
| ~ spl22_416 ),
inference(avatar_split_clause,[],[f5539,f5474,f2286,f23201]) ).
fof(f23201,plain,
( spl22_990
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| sP2(X0,X1,apply(X2,X3))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_990])]) ).
fof(f5474,plain,
( spl22_416
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| in(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_416])]) ).
fof(f5539,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| sP2(X0,X1,apply(X2,X3))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) )
| ~ spl22_230
| ~ spl22_416 ),
inference(resolution,[],[f5475,f2287]) ).
fof(f5475,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| in(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| sP2(X0,X1,apply(X2,X3)) )
| ~ spl22_416 ),
inference(avatar_component_clause,[],[f5474]) ).
fof(f23199,plain,
( spl22_989
| ~ spl22_230
| ~ spl22_415 ),
inference(avatar_split_clause,[],[f5526,f5466,f2286,f23197]) ).
fof(f23197,plain,
( spl22_989
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| sP2(X0,apply(X1,X2),X3)
| sK7(X1,sK13(X0,apply(X1,X2),X3)) = apply(X1,sK8(X1,sK13(X0,apply(X1,X2),X3)))
| apply(relation_dom_restriction(sK5,sK13(X0,apply(X1,X2),X3)),sK7(X1,sK13(X0,apply(X1,X2),X3))) = apply(sK5,sK7(X1,sK13(X0,apply(X1,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_989])]) ).
fof(f5466,plain,
( spl22_415
<=> ! [X0,X3,X2,X1] :
( sP2(X0,apply(X1,X2),X3)
| in(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_415])]) ).
fof(f5526,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| sP2(X0,apply(X1,X2),X3)
| sK7(X1,sK13(X0,apply(X1,X2),X3)) = apply(X1,sK8(X1,sK13(X0,apply(X1,X2),X3)))
| apply(relation_dom_restriction(sK5,sK13(X0,apply(X1,X2),X3)),sK7(X1,sK13(X0,apply(X1,X2),X3))) = apply(sK5,sK7(X1,sK13(X0,apply(X1,X2),X3))) )
| ~ spl22_230
| ~ spl22_415 ),
inference(resolution,[],[f5467,f2287]) ).
fof(f5467,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X1,sK13(X0,apply(X1,X2),X3))
| in(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| sP2(X0,apply(X1,X2),X3) )
| ~ spl22_415 ),
inference(avatar_component_clause,[],[f5466]) ).
fof(f23195,plain,
( spl22_988
| ~ spl22_230
| ~ spl22_414 ),
inference(avatar_split_clause,[],[f5513,f5462,f2286,f23193]) ).
fof(f23193,plain,
( spl22_988
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| sP2(X0,X1,apply(X2,X3))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_988])]) ).
fof(f5462,plain,
( spl22_414
<=> ! [X0,X3,X2,X1] :
( sP2(X0,X1,apply(X2,X3))
| in(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_414])]) ).
fof(f5513,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| sP2(X0,X1,apply(X2,X3))
| sK7(X2,sK13(X0,X1,apply(X2,X3))) = apply(X2,sK8(X2,sK13(X0,X1,apply(X2,X3))))
| apply(relation_dom_restriction(sK5,sK13(X0,X1,apply(X2,X3))),sK7(X2,sK13(X0,X1,apply(X2,X3)))) = apply(sK5,sK7(X2,sK13(X0,X1,apply(X2,X3)))) )
| ~ spl22_230
| ~ spl22_414 ),
inference(resolution,[],[f5463,f2287]) ).
fof(f5463,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X2,sK13(X0,X1,apply(X2,X3)))
| in(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| sP2(X0,X1,apply(X2,X3)) )
| ~ spl22_414 ),
inference(avatar_component_clause,[],[f5462]) ).
fof(f22335,plain,
( spl22_987
| ~ spl22_51
| ~ spl22_935 ),
inference(avatar_split_clause,[],[f20511,f18240,f494,f22333]) ).
fof(f22333,plain,
( spl22_987
<=> ! [X0] :
( one_to_one(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_987])]) ).
fof(f18240,plain,
( spl22_935
<=> ! [X150] :
( one_to_one(set_intersection2(relation_dom(sK5),X150))
| ~ empty(relation_dom_restriction(sK5,X150)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_935])]) ).
fof(f20511,plain,
( ! [X0] :
( one_to_one(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_51
| ~ spl22_935 ),
inference(superposition,[],[f18241,f495]) ).
fof(f18241,plain,
( ! [X150] :
( one_to_one(set_intersection2(relation_dom(sK5),X150))
| ~ empty(relation_dom_restriction(sK5,X150)) )
| ~ spl22_935 ),
inference(avatar_component_clause,[],[f18240]) ).
fof(f21172,plain,
( spl22_986
| ~ spl22_51
| ~ spl22_925 ),
inference(avatar_split_clause,[],[f20373,f18113,f494,f21170]) ).
fof(f21170,plain,
( spl22_986
<=> ! [X0] :
( sP1(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_986])]) ).
fof(f18113,plain,
( spl22_925
<=> ! [X88] :
( sP1(set_intersection2(relation_dom(sK5),X88))
| ~ empty(relation_dom_restriction(sK5,X88)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_925])]) ).
fof(f20373,plain,
( ! [X0] :
( sP1(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_51
| ~ spl22_925 ),
inference(superposition,[],[f18114,f495]) ).
fof(f18114,plain,
( ! [X88] :
( sP1(set_intersection2(relation_dom(sK5),X88))
| ~ empty(relation_dom_restriction(sK5,X88)) )
| ~ spl22_925 ),
inference(avatar_component_clause,[],[f18113]) ).
fof(f20656,plain,
( spl22_985
| ~ spl22_197
| ~ spl22_343 ),
inference(avatar_split_clause,[],[f3813,f3754,f1926,f20654]) ).
fof(f20654,plain,
( spl22_985
<=> ! [X0] :
( in(sK8(sK15,powerset(X0)),sK15)
| subset(sK7(sK15,powerset(X0)),X0)
| sP0(sK15,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_985])]) ).
fof(f3813,plain,
( ! [X0] :
( in(sK8(sK15,powerset(X0)),sK15)
| subset(sK7(sK15,powerset(X0)),X0)
| sP0(sK15,powerset(X0)) )
| ~ spl22_197
| ~ spl22_343 ),
inference(superposition,[],[f3755,f1928]) ).
fof(f20652,plain,
( spl22_984
| ~ spl22_56
| ~ spl22_326 ),
inference(avatar_split_clause,[],[f3692,f3388,f540,f20650]) ).
fof(f20650,plain,
( spl22_984
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_984])]) ).
fof(f3692,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_326 ),
inference(duplicate_literal_removal,[],[f3691]) ).
fof(f3691,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X11,X12,sK6(X13))
| empty(X13)
| empty(X13)
| in(sK13(X11,X12,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_326 ),
inference(resolution,[],[f3389,f541]) ).
fof(f20648,plain,
( spl22_983
| ~ spl22_51
| ~ spl22_914 ),
inference(avatar_split_clause,[],[f19936,f18069,f494,f20646]) ).
fof(f20646,plain,
( spl22_983
<=> ! [X0] :
( function(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_983])]) ).
fof(f18069,plain,
( spl22_914
<=> ! [X65] :
( function(set_intersection2(relation_dom(sK5),X65))
| ~ empty(relation_dom_restriction(sK5,X65)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_914])]) ).
fof(f19936,plain,
( ! [X0] :
( function(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_51
| ~ spl22_914 ),
inference(superposition,[],[f18070,f495]) ).
fof(f18070,plain,
( ! [X65] :
( function(set_intersection2(relation_dom(sK5),X65))
| ~ empty(relation_dom_restriction(sK5,X65)) )
| ~ spl22_914 ),
inference(avatar_component_clause,[],[f18069]) ).
fof(f20644,plain,
( spl22_982
| ~ spl22_56
| ~ spl22_324 ),
inference(avatar_split_clause,[],[f3683,f3380,f540,f20642]) ).
fof(f20642,plain,
( spl22_982
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(sK6(X12),X13,X11)
| empty(X12)
| in(sK13(sK6(X12),X13,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_982])]) ).
fof(f3683,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(sK6(X12),X13,X11)
| empty(X12)
| in(sK13(sK6(X12),X13,X11),X12) )
| ~ spl22_56
| ~ spl22_324 ),
inference(duplicate_literal_removal,[],[f3682]) ).
fof(f3682,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(sK6(X12),X13,X11)
| empty(X12)
| empty(X12)
| in(sK13(sK6(X12),X13,X11),X12) )
| ~ spl22_56
| ~ spl22_324 ),
inference(resolution,[],[f3381,f541]) ).
fof(f20640,plain,
( spl22_981
| ~ spl22_56
| ~ spl22_322 ),
inference(avatar_split_clause,[],[f3666,f3372,f540,f20638]) ).
fof(f20638,plain,
( spl22_981
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(X12,X11,sK6(X13))
| empty(X13)
| in(sK13(X12,X11,sK6(X13)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_981])]) ).
fof(f3666,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X12,X11,sK6(X13))
| empty(X13)
| in(sK13(X12,X11,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_322 ),
inference(duplicate_literal_removal,[],[f3665]) ).
fof(f3665,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X12,X11,sK6(X13))
| empty(X13)
| empty(X13)
| in(sK13(X12,X11,sK6(X13)),X13) )
| ~ spl22_56
| ~ spl22_322 ),
inference(resolution,[],[f3373,f541]) ).
fof(f20636,plain,
( spl22_980
| ~ spl22_56
| ~ spl22_320 ),
inference(avatar_split_clause,[],[f3657,f3364,f540,f20634]) ).
fof(f20634,plain,
( spl22_980
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| sP2(X12,sK6(X13),X11)
| empty(X13)
| in(sK13(X12,sK6(X13),X11),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_980])]) ).
fof(f3657,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X12,sK6(X13),X11)
| empty(X13)
| in(sK13(X12,sK6(X13),X11),X13) )
| ~ spl22_56
| ~ spl22_320 ),
inference(duplicate_literal_removal,[],[f3656]) ).
fof(f3656,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| sP2(X12,sK6(X13),X11)
| empty(X13)
| empty(X13)
| in(sK13(X12,sK6(X13),X11),X13) )
| ~ spl22_56
| ~ spl22_320 ),
inference(resolution,[],[f3365,f541]) ).
fof(f20632,plain,
( spl22_979
| ~ spl22_56
| ~ spl22_318 ),
inference(avatar_split_clause,[],[f3601,f3339,f540,f20630]) ).
fof(f20630,plain,
( spl22_979
<=> ! [X9,X8] :
( sP2(sK6(X8),X9,sK6(X8))
| empty(X8)
| in(sK13(sK6(X8),X9,sK6(X8)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_979])]) ).
fof(f3601,plain,
( ! [X8,X9] :
( sP2(sK6(X8),X9,sK6(X8))
| empty(X8)
| in(sK13(sK6(X8),X9,sK6(X8)),X8) )
| ~ spl22_56
| ~ spl22_318 ),
inference(duplicate_literal_removal,[],[f3600]) ).
fof(f3600,plain,
( ! [X8,X9] :
( sP2(sK6(X8),X9,sK6(X8))
| empty(X8)
| empty(X8)
| in(sK13(sK6(X8),X9,sK6(X8)),X8) )
| ~ spl22_56
| ~ spl22_318 ),
inference(resolution,[],[f3340,f541]) ).
fof(f20628,plain,
( spl22_978
| ~ spl22_56
| ~ spl22_316 ),
inference(avatar_split_clause,[],[f3545,f3331,f540,f20626]) ).
fof(f20626,plain,
( spl22_978
<=> ! [X9,X8] :
( sP2(X8,sK6(X9),sK6(X9))
| empty(X9)
| in(sK13(X8,sK6(X9),sK6(X9)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_978])]) ).
fof(f3545,plain,
( ! [X8,X9] :
( sP2(X8,sK6(X9),sK6(X9))
| empty(X9)
| in(sK13(X8,sK6(X9),sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_316 ),
inference(duplicate_literal_removal,[],[f3544]) ).
fof(f3544,plain,
( ! [X8,X9] :
( sP2(X8,sK6(X9),sK6(X9))
| empty(X9)
| empty(X9)
| in(sK13(X8,sK6(X9),sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_316 ),
inference(resolution,[],[f3332,f541]) ).
fof(f20624,plain,
( spl22_977
| ~ spl22_45
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3528,f3327,f448,f20622]) ).
fof(f20622,plain,
( spl22_977
<=> ! [X13,X14,X15] :
( ~ empty(X13)
| sP2(sK10(powerset(X13)),X14,X15)
| ~ in(X15,sK13(sK10(powerset(X13)),X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_977])]) ).
fof(f3528,plain,
( ! [X14,X15,X13] :
( ~ empty(X13)
| sP2(sK10(powerset(X13)),X14,X15)
| ~ in(X15,sK13(sK10(powerset(X13)),X14,X15)) )
| ~ spl22_45
| ~ spl22_315 ),
inference(resolution,[],[f3328,f449]) ).
fof(f20620,plain,
( spl22_976
| ~ spl22_45
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3511,f3323,f448,f20618]) ).
fof(f20618,plain,
( spl22_976
<=> ! [X13,X14,X15] :
( ~ empty(X13)
| sP2(X14,sK10(powerset(X13)),X15)
| ~ in(X15,sK13(X14,sK10(powerset(X13)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_976])]) ).
fof(f3511,plain,
( ! [X14,X15,X13] :
( ~ empty(X13)
| sP2(X14,sK10(powerset(X13)),X15)
| ~ in(X15,sK13(X14,sK10(powerset(X13)),X15)) )
| ~ spl22_45
| ~ spl22_314 ),
inference(resolution,[],[f3324,f449]) ).
fof(f20616,plain,
( spl22_975
| ~ spl22_45
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3494,f3319,f448,f20614]) ).
fof(f20614,plain,
( spl22_975
<=> ! [X13,X12,X14] :
( ~ empty(X12)
| sP2(X13,X14,sK10(powerset(X12)))
| ~ in(X14,sK13(X13,X14,sK10(powerset(X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_975])]) ).
fof(f3494,plain,
( ! [X14,X12,X13] :
( ~ empty(X12)
| sP2(X13,X14,sK10(powerset(X12)))
| ~ in(X14,sK13(X13,X14,sK10(powerset(X12)))) )
| ~ spl22_45
| ~ spl22_313 ),
inference(resolution,[],[f3320,f449]) ).
fof(f20612,plain,
( spl22_974
| ~ spl22_45
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3460,f3315,f448,f20610]) ).
fof(f20610,plain,
( spl22_974
<=> ! [X13,X12,X14] :
( ~ empty(X12)
| sP2(X13,X14,sK10(powerset(X12)))
| ~ in(X13,sK13(X13,X14,sK10(powerset(X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_974])]) ).
fof(f3460,plain,
( ! [X14,X12,X13] :
( ~ empty(X12)
| sP2(X13,X14,sK10(powerset(X12)))
| ~ in(X13,sK13(X13,X14,sK10(powerset(X12)))) )
| ~ spl22_45
| ~ spl22_312 ),
inference(resolution,[],[f3316,f449]) ).
fof(f20608,plain,
( spl22_973
| ~ spl22_124
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3198,f3185,f1103,f20606]) ).
fof(f20606,plain,
( spl22_973
<=> ! [X13] :
( ~ sP1(X13)
| sK10(relation_rng(X13)) = apply(X13,sK9(X13,sK10(relation_rng(X13))))
| empty(relation_rng(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_973])]) ).
fof(f3198,plain,
( ! [X13] :
( ~ sP1(X13)
| sK10(relation_rng(X13)) = apply(X13,sK9(X13,sK10(relation_rng(X13))))
| empty(relation_rng(X13)) )
| ~ spl22_124
| ~ spl22_299 ),
inference(resolution,[],[f3186,f1104]) ).
fof(f20604,plain,
( spl22_972
| ~ spl22_51
| ~ spl22_907 ),
inference(avatar_split_clause,[],[f18795,f17931,f494,f20602]) ).
fof(f20602,plain,
( spl22_972
<=> ! [X0] :
( relation(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_972])]) ).
fof(f17931,plain,
( spl22_907
<=> ! [X55] :
( relation(set_intersection2(relation_dom(sK5),X55))
| ~ empty(relation_dom_restriction(sK5,X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_907])]) ).
fof(f18795,plain,
( ! [X0] :
( relation(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_51
| ~ spl22_907 ),
inference(superposition,[],[f17932,f495]) ).
fof(f17932,plain,
( ! [X55] :
( relation(set_intersection2(relation_dom(sK5),X55))
| ~ empty(relation_dom_restriction(sK5,X55)) )
| ~ spl22_907 ),
inference(avatar_component_clause,[],[f17931]) ).
fof(f20600,plain,
( spl22_971
| ~ spl22_65
| ~ spl22_295 ),
inference(avatar_split_clause,[],[f3166,f3067,f610,f20598]) ).
fof(f20598,plain,
( spl22_971
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_971])]) ).
fof(f3166,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_295 ),
inference(resolution,[],[f3068,f611]) ).
fof(f20596,plain,
( spl22_970
| ~ spl22_65
| ~ spl22_293 ),
inference(avatar_split_clause,[],[f3161,f3059,f610,f20594]) ).
fof(f20594,plain,
( spl22_970
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(powerset(X1),X2,X0)
| ~ empty(X1)
| ~ in(X3,sK13(powerset(X1),X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_970])]) ).
fof(f3161,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(powerset(X1),X2,X0)
| ~ empty(X1)
| ~ in(X3,sK13(powerset(X1),X2,X0)) )
| ~ spl22_65
| ~ spl22_293 ),
inference(resolution,[],[f3060,f611]) ).
fof(f20592,plain,
( spl22_969
| ~ spl22_65
| ~ spl22_291 ),
inference(avatar_split_clause,[],[f3156,f3051,f610,f20590]) ).
fof(f20590,plain,
( spl22_969
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,X0,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_969])]) ).
fof(f3156,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,X0,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X1,X0,powerset(X2))) )
| ~ spl22_65
| ~ spl22_291 ),
inference(resolution,[],[f3052,f611]) ).
fof(f20588,plain,
( spl22_968
| ~ spl22_65
| ~ spl22_289 ),
inference(avatar_split_clause,[],[f3151,f3031,f610,f20586]) ).
fof(f20586,plain,
( spl22_968
<=> ! [X2,X0,X1,X3] :
( ~ empty(X0)
| sP2(X1,powerset(X2),X0)
| ~ empty(X2)
| ~ in(X3,sK13(X1,powerset(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_968])]) ).
fof(f3151,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP2(X1,powerset(X2),X0)
| ~ empty(X2)
| ~ in(X3,sK13(X1,powerset(X2),X0)) )
| ~ spl22_65
| ~ spl22_289 ),
inference(resolution,[],[f3032,f611]) ).
fof(f20584,plain,
( spl22_967
| ~ spl22_67
| ~ spl22_287 ),
inference(avatar_split_clause,[],[f3093,f3023,f633,f20582]) ).
fof(f20582,plain,
( spl22_967
<=> ! [X5,X4,X7,X6] :
( ~ sP0(X4,powerset(X5))
| ~ in(X6,relation_dom(X4))
| element(X7,X5)
| ~ in(X7,apply(X4,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_967])]) ).
fof(f3023,plain,
( spl22_287
<=> ! [X9,X8,X7] :
( ~ in(X7,relation_dom(X8))
| ~ sP0(X8,X9)
| element(apply(X8,X7),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_287])]) ).
fof(f3093,plain,
( ! [X6,X7,X4,X5] :
( ~ sP0(X4,powerset(X5))
| ~ in(X6,relation_dom(X4))
| element(X7,X5)
| ~ in(X7,apply(X4,X6)) )
| ~ spl22_67
| ~ spl22_287 ),
inference(resolution,[],[f3024,f634]) ).
fof(f3024,plain,
( ! [X8,X9,X7] :
( element(apply(X8,X7),X9)
| ~ sP0(X8,X9)
| ~ in(X7,relation_dom(X8)) )
| ~ spl22_287 ),
inference(avatar_component_clause,[],[f3023]) ).
fof(f20580,plain,
( spl22_966
| ~ spl22_67
| ~ spl22_279 ),
inference(avatar_split_clause,[],[f2998,f2963,f633,f20578]) ).
fof(f20578,plain,
( spl22_966
<=> ! [X4,X5,X3] :
( ~ empty(relation_dom(X3))
| sP0(X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_966])]) ).
fof(f2963,plain,
( spl22_279
<=> ! [X6,X5] :
( sP0(X5,X6)
| ~ empty(relation_dom(X5))
| element(sK7(X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_279])]) ).
fof(f2998,plain,
( ! [X3,X4,X5] :
( ~ empty(relation_dom(X3))
| sP0(X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) )
| ~ spl22_67
| ~ spl22_279 ),
inference(resolution,[],[f2964,f634]) ).
fof(f2964,plain,
( ! [X6,X5] :
( element(sK7(X5,X6),X6)
| ~ empty(relation_dom(X5))
| sP0(X5,X6) )
| ~ spl22_279 ),
inference(avatar_component_clause,[],[f2963]) ).
fof(f20576,plain,
( spl22_965
| ~ spl22_259
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f2988,f2959,f2727,f20574]) ).
fof(f20574,plain,
( spl22_965
<=> ! [X20,X21,X19] :
( ~ in(powerset(X19),X20)
| ~ in(powerset(X19),X21)
| ~ subset(set_intersection2(X20,X21),X19)
| empty(powerset(X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_965])]) ).
fof(f2727,plain,
( spl22_259
<=> ! [X7,X8] :
( empty(powerset(X7))
| ~ subset(X8,X7)
| ~ in(powerset(X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_259])]) ).
fof(f2988,plain,
( ! [X21,X19,X20] :
( ~ in(powerset(X19),X20)
| ~ in(powerset(X19),X21)
| ~ subset(set_intersection2(X20,X21),X19)
| empty(powerset(X19)) )
| ~ spl22_259
| ~ spl22_278 ),
inference(resolution,[],[f2960,f2728]) ).
fof(f2728,plain,
( ! [X8,X7] :
( ~ in(powerset(X7),X8)
| ~ subset(X8,X7)
| empty(powerset(X7)) )
| ~ spl22_259 ),
inference(avatar_component_clause,[],[f2727]) ).
fof(f20572,plain,
( spl22_964
| ~ spl22_65
| ~ spl22_264 ),
inference(avatar_split_clause,[],[f2886,f2747,f610,f20570]) ).
fof(f20570,plain,
( spl22_964
<=> ! [X2,X0,X1] :
( sP2(powerset(X0),X1,powerset(X0))
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_964])]) ).
fof(f2886,plain,
( ! [X2,X0,X1] :
( sP2(powerset(X0),X1,powerset(X0))
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,powerset(X0))) )
| ~ spl22_65
| ~ spl22_264 ),
inference(resolution,[],[f2748,f611]) ).
fof(f20568,plain,
( spl22_963
| ~ spl22_65
| ~ spl22_261 ),
inference(avatar_split_clause,[],[f2877,f2735,f610,f20566]) ).
fof(f20566,plain,
( spl22_963
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1),powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_963])]) ).
fof(f2877,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1),powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),powerset(X1))) )
| ~ spl22_65
| ~ spl22_261 ),
inference(resolution,[],[f2736,f611]) ).
fof(f20564,plain,
( spl22_962
| ~ spl22_67
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f2872,f2719,f633,f20562]) ).
fof(f20562,plain,
( spl22_962
<=> ! [X2,X3] :
( empty(powerset(X2))
| empty(sK6(powerset(X2)))
| element(X3,X2)
| ~ in(X3,sK10(sK6(powerset(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_962])]) ).
fof(f2719,plain,
( spl22_257
<=> ! [X4] :
( element(sK10(sK6(X4)),X4)
| empty(X4)
| empty(sK6(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_257])]) ).
fof(f2872,plain,
( ! [X2,X3] :
( empty(powerset(X2))
| empty(sK6(powerset(X2)))
| element(X3,X2)
| ~ in(X3,sK10(sK6(powerset(X2)))) )
| ~ spl22_67
| ~ spl22_257 ),
inference(resolution,[],[f2720,f634]) ).
fof(f2720,plain,
( ! [X4] :
( element(sK10(sK6(X4)),X4)
| empty(X4)
| empty(sK6(X4)) )
| ~ spl22_257 ),
inference(avatar_component_clause,[],[f2719]) ).
fof(f20560,plain,
( spl22_961
| ~ spl22_51
| ~ spl22_906 ),
inference(avatar_split_clause,[],[f18557,f17763,f494,f20558]) ).
fof(f18557,plain,
( ! [X0] :
( empty(set_intersection2(X0,relation_dom(sK5)))
| ~ empty(relation_dom_restriction(sK5,X0)) )
| ~ spl22_51
| ~ spl22_906 ),
inference(superposition,[],[f17764,f495]) ).
fof(f20556,plain,
( spl22_960
| ~ spl22_74
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2673,f2571,f668,f20554]) ).
fof(f2673,plain,
( ! [X18,X19,X17] :
( ~ sP0(X17,X18)
| ~ empty(X18)
| in(sK8(X19,relation_dom(X17)),relation_dom(X19))
| sP0(X19,relation_dom(X17)) )
| ~ spl22_74
| ~ spl22_250 ),
inference(resolution,[],[f2572,f669]) ).
fof(f20552,plain,
( spl22_959
| ~ spl22_159
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2670,f2571,f1481,f20550]) ).
fof(f2670,plain,
( ! [X10,X8,X9] :
( ~ sP0(X8,X9)
| ~ empty(X9)
| element(sK8(X10,relation_dom(X8)),relation_dom(X10))
| sP0(X10,relation_dom(X8)) )
| ~ spl22_159
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1482]) ).
fof(f20548,plain,
( spl22_958
| ~ spl22_156
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2523,f2439,f1407,f20546]) ).
fof(f20546,plain,
( spl22_958
<=> ! [X77,X78,X80,X79] :
( in(sK13(set_intersection2(X77,X78),X79,X80),X77)
| sP2(set_intersection2(X77,X78),X79,X80)
| ~ empty(X80) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_958])]) ).
fof(f2523,plain,
( ! [X80,X78,X79,X77] :
( in(sK13(set_intersection2(X77,X78),X79,X80),X77)
| sP2(set_intersection2(X77,X78),X79,X80)
| ~ empty(X80) )
| ~ spl22_156
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1408]) ).
fof(f20544,plain,
( spl22_957
| ~ spl22_154
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2519,f2439,f1399,f20542]) ).
fof(f20542,plain,
( spl22_957
<=> ! [X61,X64,X63,X62] :
( in(sK13(X61,set_intersection2(X62,X63),X64),X62)
| sP2(X61,set_intersection2(X62,X63),X64)
| ~ empty(X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_957])]) ).
fof(f2519,plain,
( ! [X62,X63,X61,X64] :
( in(sK13(X61,set_intersection2(X62,X63),X64),X62)
| sP2(X61,set_intersection2(X62,X63),X64)
| ~ empty(X64) )
| ~ spl22_154
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1400]) ).
fof(f20540,plain,
( spl22_956
| ~ spl22_157
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2512,f2439,f1411,f20538]) ).
fof(f20538,plain,
( spl22_956
<=> ! [X35,X33,X34,X36] :
( in(sK13(X33,X34,set_intersection2(X35,X36)),X35)
| sP2(X33,X34,set_intersection2(X35,X36))
| ~ empty(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_956])]) ).
fof(f2512,plain,
( ! [X36,X34,X35,X33] :
( in(sK13(X33,X34,set_intersection2(X35,X36)),X35)
| sP2(X33,X34,set_intersection2(X35,X36))
| ~ empty(X33) )
| ~ spl22_157
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1412]) ).
fof(f20536,plain,
( spl22_955
| ~ spl22_155
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2511,f2439,f1403,f20534]) ).
fof(f20534,plain,
( spl22_955
<=> ! [X31,X29,X32,X30] :
( in(sK13(X29,X30,set_intersection2(X31,X32)),X31)
| sP2(X29,X30,set_intersection2(X31,X32))
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_955])]) ).
fof(f2511,plain,
( ! [X31,X29,X32,X30] :
( in(sK13(X29,X30,set_intersection2(X31,X32)),X31)
| sP2(X29,X30,set_intersection2(X31,X32))
| ~ empty(X30) )
| ~ spl22_155
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1404]) ).
fof(f20532,plain,
( spl22_954
| ~ spl22_156
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2492,f2435,f1407,f20530]) ).
fof(f20530,plain,
( spl22_954
<=> ! [X77,X78,X80,X79] :
( in(sK13(set_intersection2(X77,X78),X79,X80),X78)
| sP2(set_intersection2(X77,X78),X79,X80)
| ~ empty(X80) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_954])]) ).
fof(f2492,plain,
( ! [X80,X78,X79,X77] :
( in(sK13(set_intersection2(X77,X78),X79,X80),X78)
| sP2(set_intersection2(X77,X78),X79,X80)
| ~ empty(X80) )
| ~ spl22_156
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1408]) ).
fof(f20528,plain,
( spl22_953
| ~ spl22_154
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2488,f2435,f1399,f20526]) ).
fof(f20526,plain,
( spl22_953
<=> ! [X61,X64,X63,X62] :
( in(sK13(X61,set_intersection2(X62,X63),X64),X63)
| sP2(X61,set_intersection2(X62,X63),X64)
| ~ empty(X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_953])]) ).
fof(f2488,plain,
( ! [X62,X63,X61,X64] :
( in(sK13(X61,set_intersection2(X62,X63),X64),X63)
| sP2(X61,set_intersection2(X62,X63),X64)
| ~ empty(X64) )
| ~ spl22_154
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1400]) ).
fof(f20524,plain,
( spl22_952
| ~ spl22_157
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2481,f2435,f1411,f20522]) ).
fof(f20522,plain,
( spl22_952
<=> ! [X35,X33,X34,X36] :
( in(sK13(X33,X34,set_intersection2(X35,X36)),X36)
| sP2(X33,X34,set_intersection2(X35,X36))
| ~ empty(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_952])]) ).
fof(f2481,plain,
( ! [X36,X34,X35,X33] :
( in(sK13(X33,X34,set_intersection2(X35,X36)),X36)
| sP2(X33,X34,set_intersection2(X35,X36))
| ~ empty(X33) )
| ~ spl22_157
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1412]) ).
fof(f20520,plain,
( spl22_951
| ~ spl22_155
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2480,f2435,f1403,f20518]) ).
fof(f20518,plain,
( spl22_951
<=> ! [X31,X29,X32,X30] :
( in(sK13(X29,X30,set_intersection2(X31,X32)),X32)
| sP2(X29,X30,set_intersection2(X31,X32))
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_951])]) ).
fof(f2480,plain,
( ! [X31,X29,X32,X30] :
( in(sK13(X29,X30,set_intersection2(X31,X32)),X32)
| sP2(X29,X30,set_intersection2(X31,X32))
| ~ empty(X30) )
| ~ spl22_155
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1404]) ).
fof(f20434,plain,
( spl22_950
| ~ spl22_230
| ~ spl22_440 ),
inference(avatar_split_clause,[],[f6249,f6151,f2286,f20432]) ).
fof(f20432,plain,
( spl22_950
<=> ! [X9,X11,X10] :
( sK7(X9,apply(X10,X11)) = apply(X9,sK8(X9,apply(X10,X11)))
| ~ in(X11,relation_dom(X10))
| sP0(X9,apply(X10,X11))
| sK7(X10,sK7(X9,apply(X10,X11))) = apply(X10,sK8(X10,sK7(X9,apply(X10,X11))))
| apply(relation_dom_restriction(sK5,sK7(X9,apply(X10,X11))),sK7(X10,sK7(X9,apply(X10,X11)))) = apply(sK5,sK7(X10,sK7(X9,apply(X10,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_950])]) ).
fof(f6151,plain,
( spl22_440
<=> ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| sK7(X0,apply(X1,X2)) = apply(X0,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK7(X0,apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_440])]) ).
fof(f6249,plain,
( ! [X10,X11,X9] :
( sK7(X9,apply(X10,X11)) = apply(X9,sK8(X9,apply(X10,X11)))
| ~ in(X11,relation_dom(X10))
| sP0(X9,apply(X10,X11))
| sK7(X10,sK7(X9,apply(X10,X11))) = apply(X10,sK8(X10,sK7(X9,apply(X10,X11))))
| apply(relation_dom_restriction(sK5,sK7(X9,apply(X10,X11))),sK7(X10,sK7(X9,apply(X10,X11)))) = apply(sK5,sK7(X10,sK7(X9,apply(X10,X11)))) )
| ~ spl22_230
| ~ spl22_440 ),
inference(resolution,[],[f6152,f2287]) ).
fof(f6152,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,sK7(X0,apply(X1,X2)))
| sK7(X0,apply(X1,X2)) = apply(X0,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1))
| sP0(X0,apply(X1,X2)) )
| ~ spl22_440 ),
inference(avatar_component_clause,[],[f6151]) ).
fof(f20394,plain,
( spl22_949
| ~ spl22_185
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2279,f2271,f1741,f20392]) ).
fof(f20392,plain,
( spl22_949
<=> ! [X18,X17,X16,X19] :
( sP2(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))
| apply(sK5,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(relation_dom_restriction(sK5,X16),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| apply(relation_dom_restriction(X18,X19),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(X18,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| ~ function(X18)
| ~ relation(X18)
| ~ function(relation_dom_restriction(X18,X19))
| ~ relation(relation_dom_restriction(X18,X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_949])]) ).
fof(f1741,plain,
( spl22_185
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_185])]) ).
fof(f2271,plain,
( spl22_229
<=> ! [X22,X21,X23] :
( sP2(X21,X22,X23)
| in(sK13(X21,X22,X23),X23)
| apply(sK5,sK13(X21,X22,X23)) = apply(relation_dom_restriction(sK5,X21),sK13(X21,X22,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_229])]) ).
fof(f2279,plain,
( ! [X18,X19,X16,X17] :
( sP2(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))
| apply(sK5,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(relation_dom_restriction(sK5,X16),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| apply(relation_dom_restriction(X18,X19),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(X18,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| ~ function(X18)
| ~ relation(X18)
| ~ function(relation_dom_restriction(X18,X19))
| ~ relation(relation_dom_restriction(X18,X19)) )
| ~ spl22_185
| ~ spl22_229 ),
inference(resolution,[],[f2272,f1742]) ).
fof(f1742,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_185 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f2272,plain,
( ! [X21,X22,X23] :
( in(sK13(X21,X22,X23),X23)
| sP2(X21,X22,X23)
| apply(sK5,sK13(X21,X22,X23)) = apply(relation_dom_restriction(sK5,X21),sK13(X21,X22,X23)) )
| ~ spl22_229 ),
inference(avatar_component_clause,[],[f2271]) ).
fof(f20390,plain,
( spl22_948
| ~ spl22_185
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2264,f2256,f1741,f20388]) ).
fof(f20388,plain,
( spl22_948
<=> ! [X18,X17,X16,X15] :
( sP2(relation_dom(relation_dom_restriction(X15,X16)),X17,X18)
| apply(relation_dom_restriction(sK5,X18),sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18)) = apply(sK5,sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18))
| apply(relation_dom_restriction(X15,X16),sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18)) = apply(X15,sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18))
| ~ function(X15)
| ~ relation(X15)
| ~ function(relation_dom_restriction(X15,X16))
| ~ relation(relation_dom_restriction(X15,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_948])]) ).
fof(f2256,plain,
( spl22_228
<=> ! [X22,X21,X23] :
( sP2(X21,X22,X23)
| in(sK13(X21,X22,X23),X21)
| apply(relation_dom_restriction(sK5,X23),sK13(X21,X22,X23)) = apply(sK5,sK13(X21,X22,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_228])]) ).
fof(f2264,plain,
( ! [X18,X16,X17,X15] :
( sP2(relation_dom(relation_dom_restriction(X15,X16)),X17,X18)
| apply(relation_dom_restriction(sK5,X18),sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18)) = apply(sK5,sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18))
| apply(relation_dom_restriction(X15,X16),sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18)) = apply(X15,sK13(relation_dom(relation_dom_restriction(X15,X16)),X17,X18))
| ~ function(X15)
| ~ relation(X15)
| ~ function(relation_dom_restriction(X15,X16))
| ~ relation(relation_dom_restriction(X15,X16)) )
| ~ spl22_185
| ~ spl22_228 ),
inference(resolution,[],[f2257,f1742]) ).
fof(f2257,plain,
( ! [X21,X22,X23] :
( in(sK13(X21,X22,X23),X21)
| sP2(X21,X22,X23)
| apply(relation_dom_restriction(sK5,X23),sK13(X21,X22,X23)) = apply(sK5,sK13(X21,X22,X23)) )
| ~ spl22_228 ),
inference(avatar_component_clause,[],[f2256]) ).
fof(f20386,plain,
( spl22_947
| ~ spl22_185
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2245,f2237,f1741,f20384]) ).
fof(f20384,plain,
( spl22_947
<=> ! [X18,X17,X16,X19] :
( sP2(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))
| apply(sK5,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(relation_dom_restriction(sK5,X17),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| apply(relation_dom_restriction(X18,X19),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(X18,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| ~ function(X18)
| ~ relation(X18)
| ~ function(relation_dom_restriction(X18,X19))
| ~ relation(relation_dom_restriction(X18,X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_947])]) ).
fof(f2237,plain,
( spl22_226
<=> ! [X22,X21,X23] :
( sP2(X21,X22,X23)
| in(sK13(X21,X22,X23),X23)
| apply(sK5,sK13(X21,X22,X23)) = apply(relation_dom_restriction(sK5,X22),sK13(X21,X22,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_226])]) ).
fof(f2245,plain,
( ! [X18,X19,X16,X17] :
( sP2(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))
| apply(sK5,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(relation_dom_restriction(sK5,X17),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| apply(relation_dom_restriction(X18,X19),sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19)))) = apply(X18,sK13(X16,X17,relation_dom(relation_dom_restriction(X18,X19))))
| ~ function(X18)
| ~ relation(X18)
| ~ function(relation_dom_restriction(X18,X19))
| ~ relation(relation_dom_restriction(X18,X19)) )
| ~ spl22_185
| ~ spl22_226 ),
inference(resolution,[],[f2238,f1742]) ).
fof(f2238,plain,
( ! [X21,X22,X23] :
( in(sK13(X21,X22,X23),X23)
| sP2(X21,X22,X23)
| apply(sK5,sK13(X21,X22,X23)) = apply(relation_dom_restriction(sK5,X22),sK13(X21,X22,X23)) )
| ~ spl22_226 ),
inference(avatar_component_clause,[],[f2237]) ).
fof(f20382,plain,
( spl22_946
| ~ spl22_185
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2230,f2222,f1741,f20380]) ).
fof(f20380,plain,
( spl22_946
<=> ! [X18,X17,X16,X15] :
( sP2(X15,relation_dom(relation_dom_restriction(X16,X17)),X18)
| apply(relation_dom_restriction(sK5,X18),sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18)) = apply(sK5,sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18))
| apply(relation_dom_restriction(X16,X17),sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18)) = apply(X16,sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18))
| ~ function(X16)
| ~ relation(X16)
| ~ function(relation_dom_restriction(X16,X17))
| ~ relation(relation_dom_restriction(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_946])]) ).
fof(f2222,plain,
( spl22_225
<=> ! [X22,X21,X23] :
( sP2(X21,X22,X23)
| in(sK13(X21,X22,X23),X22)
| apply(relation_dom_restriction(sK5,X23),sK13(X21,X22,X23)) = apply(sK5,sK13(X21,X22,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_225])]) ).
fof(f2230,plain,
( ! [X18,X16,X17,X15] :
( sP2(X15,relation_dom(relation_dom_restriction(X16,X17)),X18)
| apply(relation_dom_restriction(sK5,X18),sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18)) = apply(sK5,sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18))
| apply(relation_dom_restriction(X16,X17),sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18)) = apply(X16,sK13(X15,relation_dom(relation_dom_restriction(X16,X17)),X18))
| ~ function(X16)
| ~ relation(X16)
| ~ function(relation_dom_restriction(X16,X17))
| ~ relation(relation_dom_restriction(X16,X17)) )
| ~ spl22_185
| ~ spl22_225 ),
inference(resolution,[],[f2223,f1742]) ).
fof(f2223,plain,
( ! [X21,X22,X23] :
( in(sK13(X21,X22,X23),X22)
| sP2(X21,X22,X23)
| apply(relation_dom_restriction(sK5,X23),sK13(X21,X22,X23)) = apply(sK5,sK13(X21,X22,X23)) )
| ~ spl22_225 ),
inference(avatar_component_clause,[],[f2222]) ).
fof(f18573,plain,
( spl22_945
| ~ spl22_236
| ~ spl22_357 ),
inference(avatar_split_clause,[],[f4056,f4027,f2331,f18571]) ).
fof(f18571,plain,
( spl22_945
<=> ! [X6,X7] :
( element(sK7(X6,sK10(powerset(X7))),X7)
| sP0(X6,sK10(powerset(X7)))
| ~ sP0(X6,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_945])]) ).
fof(f4056,plain,
( ! [X6,X7] :
( element(sK7(X6,sK10(powerset(X7))),X7)
| sP0(X6,sK10(powerset(X7)))
| ~ sP0(X6,sK15) )
| ~ spl22_236
| ~ spl22_357 ),
inference(resolution,[],[f4028,f2332]) ).
fof(f18569,plain,
( spl22_944
| ~ spl22_236
| ~ spl22_348 ),
inference(avatar_split_clause,[],[f3878,f3849,f2331,f18567]) ).
fof(f18567,plain,
( spl22_944
<=> ! [X6,X7] :
( element(sK7(X6,sK6(X7)),X7)
| empty(X7)
| sP0(X6,sK6(X7))
| ~ sP0(X6,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_944])]) ).
fof(f3878,plain,
( ! [X6,X7] :
( element(sK7(X6,sK6(X7)),X7)
| empty(X7)
| sP0(X6,sK6(X7))
| ~ sP0(X6,sK15) )
| ~ spl22_236
| ~ spl22_348 ),
inference(resolution,[],[f3850,f2332]) ).
fof(f18565,plain,
( spl22_943
| ~ spl22_107
| ~ spl22_344 ),
inference(avatar_split_clause,[],[f3820,f3758,f920,f18563]) ).
fof(f18563,plain,
( spl22_943
<=> ! [X10] :
( ~ empty(X10)
| relation_rng(sK20) = X10
| sK7(sK20,X10) = apply(sK20,sK8(sK20,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_943])]) ).
fof(f920,plain,
( spl22_107
<=> sP1(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_107])]) ).
fof(f3758,plain,
( spl22_344
<=> ! [X6,X7] :
( sK7(X6,X7) = apply(X6,sK8(X6,X7))
| ~ empty(X7)
| relation_rng(X6) = X7
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_344])]) ).
fof(f3820,plain,
( ! [X10] :
( ~ empty(X10)
| relation_rng(sK20) = X10
| sK7(sK20,X10) = apply(sK20,sK8(sK20,X10)) )
| ~ spl22_107
| ~ spl22_344 ),
inference(resolution,[],[f3759,f922]) ).
fof(f922,plain,
( sP1(sK20)
| ~ spl22_107 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f3759,plain,
( ! [X6,X7] :
( ~ sP1(X6)
| ~ empty(X7)
| relation_rng(X6) = X7
| sK7(X6,X7) = apply(X6,sK8(X6,X7)) )
| ~ spl22_344 ),
inference(avatar_component_clause,[],[f3758]) ).
fof(f18489,plain,
( spl22_942
| ~ spl22_106
| ~ spl22_344 ),
inference(avatar_split_clause,[],[f3819,f3758,f915,f18487]) ).
fof(f18487,plain,
( spl22_942
<=> ! [X9] :
( ~ empty(X9)
| relation_rng(sK19) = X9
| sK7(sK19,X9) = apply(sK19,sK8(sK19,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_942])]) ).
fof(f915,plain,
( spl22_106
<=> sP1(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_106])]) ).
fof(f3819,plain,
( ! [X9] :
( ~ empty(X9)
| relation_rng(sK19) = X9
| sK7(sK19,X9) = apply(sK19,sK8(sK19,X9)) )
| ~ spl22_106
| ~ spl22_344 ),
inference(resolution,[],[f3759,f917]) ).
fof(f917,plain,
( sP1(sK19)
| ~ spl22_106 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f18485,plain,
( spl22_941
| ~ spl22_250
| ~ spl22_343 ),
inference(avatar_split_clause,[],[f3805,f3754,f2571,f18483]) ).
fof(f18483,plain,
( spl22_941
<=> ! [X4,X5,X3] :
( subset(sK7(X3,powerset(X4)),X4)
| sP0(X3,powerset(X4))
| ~ sP0(X3,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_941])]) ).
fof(f3805,plain,
( ! [X3,X4,X5] :
( subset(sK7(X3,powerset(X4)),X4)
| sP0(X3,powerset(X4))
| ~ sP0(X3,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_343 ),
inference(resolution,[],[f3755,f2572]) ).
fof(f18481,plain,
( spl22_940
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3799,f3750,f812,f249,f433,f18479]) ).
fof(f18479,plain,
( spl22_940
<=> ! [X10] :
( apply(sK15,sK15) = apply(relation_dom_restriction(sK15,powerset(X10)),sK15)
| empty(powerset(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_940])]) ).
fof(f3799,plain,
( ! [X10] :
( ~ function(sK15)
| apply(sK15,sK15) = apply(relation_dom_restriction(sK15,powerset(X10)),sK15)
| empty(powerset(X10)) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_342 ),
inference(forward_demodulation,[],[f3798,f814]) ).
fof(f3798,plain,
( ! [X10] :
( apply(sK15,sK15) = apply(relation_dom_restriction(sK15,powerset(X10)),sK15)
| ~ function(empty_set)
| empty(powerset(X10)) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_342 ),
inference(forward_demodulation,[],[f3789,f814]) ).
fof(f3789,plain,
( ! [X10] :
( apply(relation_dom_restriction(empty_set,powerset(X10)),sK15) = apply(empty_set,sK15)
| ~ function(empty_set)
| empty(powerset(X10)) )
| ~ spl22_7
| ~ spl22_342 ),
inference(resolution,[],[f3751,f251]) ).
fof(f18411,plain,
( ~ spl22_20
| spl22_939
| ~ spl22_19
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3796,f3750,f309,f18409,f314]) ).
fof(f18409,plain,
( spl22_939
<=> ! [X17] :
( apply(relation_dom_restriction(sK20,powerset(X17)),sK15) = apply(sK20,sK15)
| empty(powerset(X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_939])]) ).
fof(f3796,plain,
( ! [X17] :
( apply(relation_dom_restriction(sK20,powerset(X17)),sK15) = apply(sK20,sK15)
| ~ function(sK20)
| empty(powerset(X17)) )
| ~ spl22_19
| ~ spl22_342 ),
inference(resolution,[],[f3751,f311]) ).
fof(f18341,plain,
( ~ spl22_18
| spl22_938
| ~ spl22_17
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3795,f3750,f299,f18339,f304]) ).
fof(f18339,plain,
( spl22_938
<=> ! [X16] :
( apply(relation_dom_restriction(sK19,powerset(X16)),sK15) = apply(sK19,sK15)
| empty(powerset(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_938])]) ).
fof(f3795,plain,
( ! [X16] :
( apply(relation_dom_restriction(sK19,powerset(X16)),sK15) = apply(sK19,sK15)
| ~ function(sK19)
| empty(powerset(X16)) )
| ~ spl22_17
| ~ spl22_342 ),
inference(resolution,[],[f3751,f301]) ).
fof(f18337,plain,
( spl22_937
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3780,f3746,f812,f249,f433,f18335]) ).
fof(f18335,plain,
( spl22_937
<=> ! [X10] :
( apply(relation_dom_restriction(sK15,X10),sK10(X10)) = apply(sK15,sK10(X10))
| empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_937])]) ).
fof(f3780,plain,
( ! [X10] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X10),sK10(X10)) = apply(sK15,sK10(X10))
| empty(X10) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_341 ),
inference(forward_demodulation,[],[f3779,f814]) ).
fof(f3779,plain,
( ! [X10] :
( apply(relation_dom_restriction(sK15,X10),sK10(X10)) = apply(sK15,sK10(X10))
| ~ function(empty_set)
| empty(X10) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_341 ),
inference(forward_demodulation,[],[f3770,f814]) ).
fof(f3770,plain,
( ! [X10] :
( apply(relation_dom_restriction(empty_set,X10),sK10(X10)) = apply(empty_set,sK10(X10))
| ~ function(empty_set)
| empty(X10) )
| ~ spl22_7
| ~ spl22_341 ),
inference(resolution,[],[f3747,f251]) ).
fof(f18246,plain,
( ~ spl22_20
| spl22_936
| ~ spl22_19
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3777,f3746,f309,f18244,f314]) ).
fof(f3777,plain,
( ! [X17] :
( apply(relation_dom_restriction(sK20,X17),sK10(X17)) = apply(sK20,sK10(X17))
| ~ function(sK20)
| empty(X17) )
| ~ spl22_19
| ~ spl22_341 ),
inference(resolution,[],[f3747,f311]) ).
fof(f18242,plain,
( spl22_935
| ~ spl22_535
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15120,f15007,f7326,f18240]) ).
fof(f7326,plain,
( spl22_535
<=> ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_535])]) ).
fof(f15120,plain,
( ! [X150] :
( one_to_one(set_intersection2(relation_dom(sK5),X150))
| ~ empty(relation_dom_restriction(sK5,X150)) )
| ~ spl22_535
| ~ spl22_823 ),
inference(superposition,[],[f7327,f15008]) ).
fof(f7327,plain,
( ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_535 ),
inference(avatar_component_clause,[],[f7326]) ).
fof(f18151,plain,
( ~ spl22_18
| spl22_934
| ~ spl22_17
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3776,f3746,f299,f18149,f304]) ).
fof(f3776,plain,
( ! [X16] :
( apply(relation_dom_restriction(sK19,X16),sK10(X16)) = apply(sK19,sK10(X16))
| ~ function(sK19)
| empty(X16) )
| ~ spl22_17
| ~ spl22_341 ),
inference(resolution,[],[f3747,f301]) ).
fof(f18147,plain,
( spl22_933
| ~ spl22_56
| ~ spl22_309 ),
inference(avatar_split_clause,[],[f3309,f3268,f540,f18145]) ).
fof(f18145,plain,
( spl22_933
<=> ! [X11,X12,X13] :
( ~ sP0(X11,sK6(X12))
| ~ in(X13,relation_dom(X11))
| empty(X12)
| in(apply(X11,X13),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_933])]) ).
fof(f3309,plain,
( ! [X11,X12,X13] :
( ~ sP0(X11,sK6(X12))
| ~ in(X13,relation_dom(X11))
| empty(X12)
| in(apply(X11,X13),X12) )
| ~ spl22_56
| ~ spl22_309 ),
inference(duplicate_literal_removal,[],[f3299]) ).
fof(f3299,plain,
( ! [X11,X12,X13] :
( ~ sP0(X11,sK6(X12))
| ~ in(X13,relation_dom(X11))
| empty(X12)
| empty(X12)
| in(apply(X11,X13),X12) )
| ~ spl22_56
| ~ spl22_309 ),
inference(resolution,[],[f3269,f541]) ).
fof(f18143,plain,
( spl22_932
| ~ spl22_56
| ~ spl22_307 ),
inference(avatar_split_clause,[],[f3287,f3260,f540,f18141]) ).
fof(f18141,plain,
( spl22_932
<=> ! [X9,X8] :
( ~ empty(relation_dom(X8))
| sP0(X8,sK6(X9))
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_932])]) ).
fof(f3287,plain,
( ! [X8,X9] :
( ~ empty(relation_dom(X8))
| sP0(X8,sK6(X9))
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_307 ),
inference(duplicate_literal_removal,[],[f3286]) ).
fof(f3286,plain,
( ! [X8,X9] :
( ~ empty(relation_dom(X8))
| sP0(X8,sK6(X9))
| empty(X9)
| empty(X9)
| in(sK7(X8,sK6(X9)),X9) )
| ~ spl22_56
| ~ spl22_307 ),
inference(resolution,[],[f3261,f541]) ).
fof(f18139,plain,
( spl22_931
| ~ spl22_45
| ~ spl22_306 ),
inference(avatar_split_clause,[],[f3281,f3256,f448,f18137]) ).
fof(f18137,plain,
( spl22_931
<=> ! [X16,X15] :
( ~ empty(X15)
| sP0(X16,sK10(powerset(X15)))
| ~ in(relation_dom(X16),sK8(X16,sK10(powerset(X15)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_931])]) ).
fof(f3256,plain,
( spl22_306
<=> ! [X2,X3] :
( ~ empty(X2)
| in(sK8(X3,sK10(powerset(X2))),relation_dom(X3))
| sP0(X3,sK10(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_306])]) ).
fof(f3281,plain,
( ! [X16,X15] :
( ~ empty(X15)
| sP0(X16,sK10(powerset(X15)))
| ~ in(relation_dom(X16),sK8(X16,sK10(powerset(X15)))) )
| ~ spl22_45
| ~ spl22_306 ),
inference(resolution,[],[f3257,f449]) ).
fof(f3257,plain,
( ! [X2,X3] :
( in(sK8(X3,sK10(powerset(X2))),relation_dom(X3))
| ~ empty(X2)
| sP0(X3,sK10(powerset(X2))) )
| ~ spl22_306 ),
inference(avatar_component_clause,[],[f3256]) ).
fof(f18135,plain,
( spl22_930
| ~ spl22_65
| ~ spl22_287 ),
inference(avatar_split_clause,[],[f3092,f3023,f610,f18133]) ).
fof(f18133,plain,
( spl22_930
<=> ! [X2,X0,X1,X3] :
( ~ sP0(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_930])]) ).
fof(f3092,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) )
| ~ spl22_65
| ~ spl22_287 ),
inference(resolution,[],[f3024,f611]) ).
fof(f18131,plain,
( spl22_929
| ~ spl22_62
| ~ spl22_285 ),
inference(avatar_split_clause,[],[f3080,f3015,f598,f18129]) ).
fof(f18129,plain,
( spl22_929
<=> ! [X4] :
( sK7(X4,sK15) = apply(X4,sK8(X4,sK15))
| sK15 = relation_rng(X4)
| ~ sP1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_929])]) ).
fof(f3015,plain,
( spl22_285
<=> ! [X0] :
( sK7(X0,sK15) = apply(X0,sK8(X0,sK15))
| sP0(X0,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_285])]) ).
fof(f3080,plain,
( ! [X4] :
( sK7(X4,sK15) = apply(X4,sK8(X4,sK15))
| sK15 = relation_rng(X4)
| ~ sP1(X4) )
| ~ spl22_62
| ~ spl22_285 ),
inference(resolution,[],[f3016,f599]) ).
fof(f3016,plain,
( ! [X0] :
( sP0(X0,sK15)
| sK7(X0,sK15) = apply(X0,sK8(X0,sK15)) )
| ~ spl22_285 ),
inference(avatar_component_clause,[],[f3015]) ).
fof(f18127,plain,
( spl22_928
| ~ spl22_65
| ~ spl22_279 ),
inference(avatar_split_clause,[],[f2997,f2963,f610,f18125]) ).
fof(f18125,plain,
( spl22_928
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_928])]) ).
fof(f2997,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_279 ),
inference(resolution,[],[f2964,f611]) ).
fof(f18123,plain,
( spl22_927
| ~ spl22_67
| ~ spl22_275 ),
inference(avatar_split_clause,[],[f2932,f2795,f633,f18121]) ).
fof(f18121,plain,
( spl22_927
<=> ! [X4,X5,X3] :
( sP2(powerset(X3),X4,sK15)
| element(X5,X3)
| ~ in(X5,sK13(powerset(X3),X4,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_927])]) ).
fof(f2795,plain,
( spl22_275
<=> ! [X25,X26] :
( element(sK13(X25,X26,sK15),X25)
| sP2(X25,X26,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_275])]) ).
fof(f2932,plain,
( ! [X3,X4,X5] :
( sP2(powerset(X3),X4,sK15)
| element(X5,X3)
| ~ in(X5,sK13(powerset(X3),X4,sK15)) )
| ~ spl22_67
| ~ spl22_275 ),
inference(resolution,[],[f2796,f634]) ).
fof(f2796,plain,
( ! [X26,X25] :
( element(sK13(X25,X26,sK15),X25)
| sP2(X25,X26,sK15) )
| ~ spl22_275 ),
inference(avatar_component_clause,[],[f2795]) ).
fof(f18119,plain,
( spl22_926
| ~ spl22_67
| ~ spl22_274 ),
inference(avatar_split_clause,[],[f2925,f2791,f633,f18117]) ).
fof(f18117,plain,
( spl22_926
<=> ! [X4,X5,X3] :
( sP2(sK15,X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(sK15,X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_926])]) ).
fof(f2791,plain,
( spl22_274
<=> ! [X25,X24] :
( element(sK13(sK15,X24,X25),X25)
| sP2(sK15,X24,X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_274])]) ).
fof(f2925,plain,
( ! [X3,X4,X5] :
( sP2(sK15,X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(sK15,X3,powerset(X4))) )
| ~ spl22_67
| ~ spl22_274 ),
inference(resolution,[],[f2792,f634]) ).
fof(f2792,plain,
( ! [X24,X25] :
( element(sK13(sK15,X24,X25),X25)
| sP2(sK15,X24,X25) )
| ~ spl22_274 ),
inference(avatar_component_clause,[],[f2791]) ).
fof(f18115,plain,
( spl22_925
| ~ spl22_209
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15090,f15007,f2032,f18113]) ).
fof(f2032,plain,
( spl22_209
<=> ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_209])]) ).
fof(f15090,plain,
( ! [X88] :
( sP1(set_intersection2(relation_dom(sK5),X88))
| ~ empty(relation_dom_restriction(sK5,X88)) )
| ~ spl22_209
| ~ spl22_823 ),
inference(superposition,[],[f2033,f15008]) ).
fof(f2033,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_209 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f18111,plain,
( spl22_924
| ~ spl22_67
| ~ spl22_273 ),
inference(avatar_split_clause,[],[f2921,f2787,f633,f18109]) ).
fof(f18109,plain,
( spl22_924
<=> ! [X4,X5,X3] :
( sP2(X3,powerset(X4),sK15)
| element(X5,X4)
| ~ in(X5,sK13(X3,powerset(X4),sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_924])]) ).
fof(f2787,plain,
( spl22_273
<=> ! [X25,X26] :
( element(sK13(X25,X26,sK15),X26)
| sP2(X25,X26,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_273])]) ).
fof(f2921,plain,
( ! [X3,X4,X5] :
( sP2(X3,powerset(X4),sK15)
| element(X5,X4)
| ~ in(X5,sK13(X3,powerset(X4),sK15)) )
| ~ spl22_67
| ~ spl22_273 ),
inference(resolution,[],[f2788,f634]) ).
fof(f2788,plain,
( ! [X26,X25] :
( element(sK13(X25,X26,sK15),X26)
| sP2(X25,X26,sK15) )
| ~ spl22_273 ),
inference(avatar_component_clause,[],[f2787]) ).
fof(f18107,plain,
( spl22_923
| ~ spl22_67
| ~ spl22_272 ),
inference(avatar_split_clause,[],[f2917,f2783,f633,f18105]) ).
fof(f18105,plain,
( spl22_923
<=> ! [X4,X5,X3] :
( sP2(X3,sK15,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(X3,sK15,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_923])]) ).
fof(f2783,plain,
( spl22_272
<=> ! [X25,X24] :
( element(sK13(X24,sK15,X25),X25)
| sP2(X24,sK15,X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_272])]) ).
fof(f2917,plain,
( ! [X3,X4,X5] :
( sP2(X3,sK15,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK13(X3,sK15,powerset(X4))) )
| ~ spl22_67
| ~ spl22_272 ),
inference(resolution,[],[f2784,f634]) ).
fof(f2784,plain,
( ! [X24,X25] :
( element(sK13(X24,sK15,X25),X25)
| sP2(X24,sK15,X25) )
| ~ spl22_272 ),
inference(avatar_component_clause,[],[f2783]) ).
fof(f18103,plain,
( spl22_922
| ~ spl22_65
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f2871,f2719,f610,f18101]) ).
fof(f18101,plain,
( spl22_922
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_922])]) ).
fof(f2871,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK6(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK10(sK6(powerset(X0)))) )
| ~ spl22_65
| ~ spl22_257 ),
inference(resolution,[],[f2720,f611]) ).
fof(f18099,plain,
( spl22_921
| ~ spl22_67
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2868,f2715,f633,f18097]) ).
fof(f18097,plain,
( spl22_921
<=> ! [X2,X3] :
( empty(sK10(powerset(powerset(X2))))
| element(X3,X2)
| ~ in(X3,sK10(sK10(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_921])]) ).
fof(f2715,plain,
( spl22_256
<=> ! [X4] :
( element(sK10(sK10(powerset(X4))),X4)
| empty(sK10(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_256])]) ).
fof(f2868,plain,
( ! [X2,X3] :
( empty(sK10(powerset(powerset(X2))))
| element(X3,X2)
| ~ in(X3,sK10(sK10(powerset(powerset(X2))))) )
| ~ spl22_67
| ~ spl22_256 ),
inference(resolution,[],[f2716,f634]) ).
fof(f2716,plain,
( ! [X4] :
( element(sK10(sK10(powerset(X4))),X4)
| empty(sK10(powerset(X4))) )
| ~ spl22_256 ),
inference(avatar_component_clause,[],[f2715]) ).
fof(f18095,plain,
( spl22_920
| ~ spl22_149
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2505,f2439,f1362,f18093]) ).
fof(f18093,plain,
( spl22_920
<=> ! [X12,X11,X10] :
( in(sK7(X10,set_intersection2(X11,X12)),X11)
| sP0(X10,set_intersection2(X11,X12))
| ~ empty(relation_dom(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_920])]) ).
fof(f2505,plain,
( ! [X10,X11,X12] :
( in(sK7(X10,set_intersection2(X11,X12)),X11)
| sP0(X10,set_intersection2(X11,X12))
| ~ empty(relation_dom(X10)) )
| ~ spl22_149
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1363]) ).
fof(f18091,plain,
( spl22_919
| ~ spl22_149
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2474,f2435,f1362,f18089]) ).
fof(f18089,plain,
( spl22_919
<=> ! [X11,X12,X10] :
( in(sK7(X10,set_intersection2(X11,X12)),X12)
| sP0(X10,set_intersection2(X11,X12))
| ~ empty(relation_dom(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_919])]) ).
fof(f2474,plain,
( ! [X10,X11,X12] :
( in(sK7(X10,set_intersection2(X11,X12)),X12)
| sP0(X10,set_intersection2(X11,X12))
| ~ empty(relation_dom(X10)) )
| ~ spl22_149
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1363]) ).
fof(f18087,plain,
( spl22_918
| ~ spl22_78
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2430,f2331,f692,f18085]) ).
fof(f18085,plain,
( spl22_918
<=> ! [X69,X68,X67] :
( ~ sP0(X67,sK15)
| in(sK13(relation_dom(X67),X68,X69),X69)
| sP2(relation_dom(X67),X68,X69) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_918])]) ).
fof(f2430,plain,
( ! [X68,X69,X67] :
( ~ sP0(X67,sK15)
| in(sK13(relation_dom(X67),X68,X69),X69)
| sP2(relation_dom(X67),X68,X69) )
| ~ spl22_78
| ~ spl22_236 ),
inference(resolution,[],[f2332,f693]) ).
fof(f18083,plain,
( spl22_917
| ~ spl22_170
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2428,f2331,f1550,f18081]) ).
fof(f18081,plain,
( spl22_917
<=> ! [X61,X62,X63] :
( ~ sP0(X61,sK15)
| element(sK13(relation_dom(X61),X62,X63),X63)
| sP2(relation_dom(X61),X62,X63) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_917])]) ).
fof(f2428,plain,
( ! [X62,X63,X61] :
( ~ sP0(X61,sK15)
| element(sK13(relation_dom(X61),X62,X63),X63)
| sP2(relation_dom(X61),X62,X63) )
| ~ spl22_170
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1551]) ).
fof(f18079,plain,
( spl22_916
| ~ spl22_77
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2426,f2331,f688,f18077]) ).
fof(f18077,plain,
( spl22_916
<=> ! [X57,X55,X56] :
( ~ sP0(X55,sK15)
| in(sK13(X56,relation_dom(X55),X57),X57)
| sP2(X56,relation_dom(X55),X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_916])]) ).
fof(f2426,plain,
( ! [X56,X57,X55] :
( ~ sP0(X55,sK15)
| in(sK13(X56,relation_dom(X55),X57),X57)
| sP2(X56,relation_dom(X55),X57) )
| ~ spl22_77
| ~ spl22_236 ),
inference(resolution,[],[f2332,f689]) ).
fof(f18075,plain,
( spl22_915
| ~ spl22_166
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2424,f2331,f1533,f18073]) ).
fof(f18073,plain,
( spl22_915
<=> ! [X50,X51,X49] :
( ~ sP0(X49,sK15)
| element(sK13(X50,relation_dom(X49),X51),X51)
| sP2(X50,relation_dom(X49),X51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_915])]) ).
fof(f2424,plain,
( ! [X50,X51,X49] :
( ~ sP0(X49,sK15)
| element(sK13(X50,relation_dom(X49),X51),X51)
| sP2(X50,relation_dom(X49),X51) )
| ~ spl22_166
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1534]) ).
fof(f18071,plain,
( spl22_914
| ~ spl22_111
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15079,f15007,f940,f18069]) ).
fof(f940,plain,
( spl22_111
<=> ! [X2] :
( ~ empty(X2)
| function(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_111])]) ).
fof(f15079,plain,
( ! [X65] :
( function(set_intersection2(relation_dom(sK5),X65))
| ~ empty(relation_dom_restriction(sK5,X65)) )
| ~ spl22_111
| ~ spl22_823 ),
inference(superposition,[],[f941,f15008]) ).
fof(f941,plain,
( ! [X2] :
( function(relation_dom(X2))
| ~ empty(X2) )
| ~ spl22_111 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f18067,plain,
( spl22_913
| ~ spl22_172
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2420,f2331,f1558,f18065]) ).
fof(f18065,plain,
( spl22_913
<=> ! [X38,X37,X39] :
( ~ sP0(X37,sK15)
| element(sK13(X38,X39,relation_dom(X37)),X38)
| sP2(X38,X39,relation_dom(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_913])]) ).
fof(f2420,plain,
( ! [X38,X39,X37] :
( ~ sP0(X37,sK15)
| element(sK13(X38,X39,relation_dom(X37)),X38)
| sP2(X38,X39,relation_dom(X37)) )
| ~ spl22_172
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1559]) ).
fof(f18063,plain,
( spl22_912
| ~ spl22_168
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2419,f2331,f1542,f18061]) ).
fof(f18061,plain,
( spl22_912
<=> ! [X34,X36,X35] :
( ~ sP0(X34,sK15)
| element(sK13(X35,X36,relation_dom(X34)),X36)
| sP2(X35,X36,relation_dom(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_912])]) ).
fof(f2419,plain,
( ! [X36,X34,X35] :
( ~ sP0(X34,sK15)
| element(sK13(X35,X36,relation_dom(X34)),X36)
| sP2(X35,X36,relation_dom(X34)) )
| ~ spl22_168
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1543]) ).
fof(f18059,plain,
( spl22_911
| ~ spl22_78
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2416,f2331,f692,f18057]) ).
fof(f18057,plain,
( spl22_911
<=> ! [X25,X27,X26] :
( ~ sP0(X25,sK15)
| in(sK13(X26,X27,relation_dom(X25)),X26)
| sP2(X26,X27,relation_dom(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_911])]) ).
fof(f2416,plain,
( ! [X26,X27,X25] :
( ~ sP0(X25,sK15)
| in(sK13(X26,X27,relation_dom(X25)),X26)
| sP2(X26,X27,relation_dom(X25)) )
| ~ spl22_78
| ~ spl22_236 ),
inference(resolution,[],[f2332,f693]) ).
fof(f18055,plain,
( spl22_910
| ~ spl22_77
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2415,f2331,f688,f18053]) ).
fof(f18053,plain,
( spl22_910
<=> ! [X22,X24,X23] :
( ~ sP0(X22,sK15)
| in(sK13(X23,X24,relation_dom(X22)),X24)
| sP2(X23,X24,relation_dom(X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_910])]) ).
fof(f2415,plain,
( ! [X24,X22,X23] :
( ~ sP0(X22,sK15)
| in(sK13(X23,X24,relation_dom(X22)),X24)
| sP2(X23,X24,relation_dom(X22)) )
| ~ spl22_77
| ~ spl22_236 ),
inference(resolution,[],[f2332,f689]) ).
fof(f18006,plain,
( spl22_909
| ~ spl22_230
| ~ spl22_397 ),
inference(avatar_split_clause,[],[f5287,f5079,f2286,f18004]) ).
fof(f18004,plain,
( spl22_909
<=> ! [X2,X0,X1] :
( in(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| sP0(X0,apply(X1,X2))
| sK7(X1,sK7(X0,apply(X1,X2))) = apply(X1,sK8(X1,sK7(X0,apply(X1,X2))))
| apply(relation_dom_restriction(sK5,sK7(X0,apply(X1,X2))),sK7(X1,sK7(X0,apply(X1,X2)))) = apply(sK5,sK7(X1,sK7(X0,apply(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_909])]) ).
fof(f5079,plain,
( spl22_397
<=> ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| in(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK7(X0,apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_397])]) ).
fof(f5287,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| sP0(X0,apply(X1,X2))
| sK7(X1,sK7(X0,apply(X1,X2))) = apply(X1,sK8(X1,sK7(X0,apply(X1,X2))))
| apply(relation_dom_restriction(sK5,sK7(X0,apply(X1,X2))),sK7(X1,sK7(X0,apply(X1,X2)))) = apply(sK5,sK7(X1,sK7(X0,apply(X1,X2)))) )
| ~ spl22_230
| ~ spl22_397 ),
inference(resolution,[],[f5080,f2287]) ).
fof(f5080,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,sK7(X0,apply(X1,X2)))
| in(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| sP0(X0,apply(X1,X2)) )
| ~ spl22_397 ),
inference(avatar_component_clause,[],[f5079]) ).
fof(f17945,plain,
( spl22_908
| ~ spl22_185
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2096,f2089,f1741,f17943]) ).
fof(f17943,plain,
( spl22_908
<=> ! [X9,X11,X10] :
( sP0(X9,relation_dom(relation_dom_restriction(X10,X11)))
| apply(relation_dom_restriction(sK5,relation_dom(X9)),sK8(X9,relation_dom(relation_dom_restriction(X10,X11)))) = apply(sK5,sK8(X9,relation_dom(relation_dom_restriction(X10,X11))))
| apply(relation_dom_restriction(X10,X11),sK7(X9,relation_dom(relation_dom_restriction(X10,X11)))) = apply(X10,sK7(X9,relation_dom(relation_dom_restriction(X10,X11))))
| ~ function(X10)
| ~ relation(X10)
| ~ function(relation_dom_restriction(X10,X11))
| ~ relation(relation_dom_restriction(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_908])]) ).
fof(f2089,plain,
( spl22_212
<=> ! [X16,X17] :
( apply(relation_dom_restriction(sK5,relation_dom(X16)),sK8(X16,X17)) = apply(sK5,sK8(X16,X17))
| sP0(X16,X17)
| in(sK7(X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_212])]) ).
fof(f2096,plain,
( ! [X10,X11,X9] :
( sP0(X9,relation_dom(relation_dom_restriction(X10,X11)))
| apply(relation_dom_restriction(sK5,relation_dom(X9)),sK8(X9,relation_dom(relation_dom_restriction(X10,X11)))) = apply(sK5,sK8(X9,relation_dom(relation_dom_restriction(X10,X11))))
| apply(relation_dom_restriction(X10,X11),sK7(X9,relation_dom(relation_dom_restriction(X10,X11)))) = apply(X10,sK7(X9,relation_dom(relation_dom_restriction(X10,X11))))
| ~ function(X10)
| ~ relation(X10)
| ~ function(relation_dom_restriction(X10,X11))
| ~ relation(relation_dom_restriction(X10,X11)) )
| ~ spl22_185
| ~ spl22_212 ),
inference(resolution,[],[f2090,f1742]) ).
fof(f2090,plain,
( ! [X16,X17] :
( in(sK7(X16,X17),X17)
| sP0(X16,X17)
| apply(relation_dom_restriction(sK5,relation_dom(X16)),sK8(X16,X17)) = apply(sK5,sK8(X16,X17)) )
| ~ spl22_212 ),
inference(avatar_component_clause,[],[f2089]) ).
fof(f17933,plain,
( spl22_907
| ~ spl22_37
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15074,f15007,f397,f17931]) ).
fof(f15074,plain,
( ! [X55] :
( relation(set_intersection2(relation_dom(sK5),X55))
| ~ empty(relation_dom_restriction(sK5,X55)) )
| ~ spl22_37
| ~ spl22_823 ),
inference(superposition,[],[f398,f15008]) ).
fof(f17765,plain,
( spl22_906
| ~ spl22_36
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15073,f15007,f393,f17763]) ).
fof(f15073,plain,
( ! [X54] :
( empty(set_intersection2(relation_dom(sK5),X54))
| ~ empty(relation_dom_restriction(sK5,X54)) )
| ~ spl22_36
| ~ spl22_823 ),
inference(superposition,[],[f394,f15008]) ).
fof(f16935,plain,
( ~ spl22_904
| spl22_905
| ~ spl22_501
| ~ spl22_533 ),
inference(avatar_split_clause,[],[f16045,f7314,f6994,f16932,f16928]) ).
fof(f16928,plain,
( spl22_904
<=> empty(relation_dom_restriction(sK5,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_904])]) ).
fof(f16932,plain,
( spl22_905
<=> in(apply(sK5,sK4),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_905])]) ).
fof(f7314,plain,
( spl22_533
<=> ! [X0] :
( sP0(X0,sK15)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_533])]) ).
fof(f16045,plain,
( in(apply(sK5,sK4),sK15)
| ~ empty(relation_dom_restriction(sK5,sK3))
| ~ spl22_501
| ~ spl22_533 ),
inference(resolution,[],[f6995,f7315]) ).
fof(f7315,plain,
( ! [X0] :
( sP0(X0,sK15)
| ~ empty(X0) )
| ~ spl22_533 ),
inference(avatar_component_clause,[],[f7314]) ).
fof(f16514,plain,
( spl22_903
| ~ spl22_388 ),
inference(avatar_split_clause,[],[f4936,f4594,f16512]) ).
fof(f16512,plain,
( spl22_903
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X0))),X0)
| sP2(X0,X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_903])]) ).
fof(f4936,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X0))),X0)
| sP2(X0,X1,sK10(powerset(X0))) )
| ~ spl22_388 ),
inference(factoring,[],[f4595]) ).
fof(f16510,plain,
( spl22_902
| ~ spl22_386 ),
inference(avatar_split_clause,[],[f4881,f4586,f16508]) ).
fof(f16508,plain,
( spl22_902
<=> ! [X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X0),X0)
| sP2(sK10(powerset(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_902])]) ).
fof(f4881,plain,
( ! [X0,X1] :
( element(sK13(sK10(powerset(X0)),X1,X0),X0)
| sP2(sK10(powerset(X0)),X1,X0) )
| ~ spl22_386 ),
inference(factoring,[],[f4587]) ).
fof(f16506,plain,
( spl22_901
| ~ spl22_383 ),
inference(avatar_split_clause,[],[f4826,f4574,f16504]) ).
fof(f16504,plain,
( spl22_901
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X1))),X1)
| sP2(X0,X1,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_901])]) ).
fof(f4826,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK10(powerset(X1))),X1)
| sP2(X0,X1,sK10(powerset(X1))) )
| ~ spl22_383 ),
inference(factoring,[],[f4575]) ).
fof(f16502,plain,
( spl22_900
| ~ spl22_381 ),
inference(avatar_split_clause,[],[f4767,f4566,f16500]) ).
fof(f16500,plain,
( spl22_900
<=> ! [X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X1),X1)
| sP2(X0,sK10(powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_900])]) ).
fof(f4767,plain,
( ! [X0,X1] :
( element(sK13(X0,sK10(powerset(X1)),X1),X1)
| sP2(X0,sK10(powerset(X1)),X1) )
| ~ spl22_381 ),
inference(factoring,[],[f4567]) ).
fof(f16497,plain,
( spl22_899
| ~ spl22_374 ),
inference(avatar_split_clause,[],[f4540,f4168,f16495]) ).
fof(f16495,plain,
( spl22_899
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK6(X0)),X0)
| sP2(X0,X1,sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_899])]) ).
fof(f4540,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK6(X0)),X0)
| sP2(X0,X1,sK6(X0))
| empty(X0) )
| ~ spl22_374 ),
inference(factoring,[],[f4169]) ).
fof(f16493,plain,
( spl22_898
| ~ spl22_372 ),
inference(avatar_split_clause,[],[f4449,f4160,f16491]) ).
fof(f16491,plain,
( spl22_898
<=> ! [X0,X1] :
( element(sK13(sK6(X0),X1,X0),X0)
| sP2(sK6(X0),X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_898])]) ).
fof(f4449,plain,
( ! [X0,X1] :
( element(sK13(sK6(X0),X1,X0),X0)
| sP2(sK6(X0),X1,X0)
| empty(X0) )
| ~ spl22_372 ),
inference(factoring,[],[f4161]) ).
fof(f16489,plain,
( spl22_897
| ~ spl22_370 ),
inference(avatar_split_clause,[],[f4398,f4152,f16487]) ).
fof(f16487,plain,
( spl22_897
<=> ! [X0,X1] :
( element(sK13(X0,X1,sK6(X1)),X1)
| sP2(X0,X1,sK6(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_897])]) ).
fof(f4398,plain,
( ! [X0,X1] :
( element(sK13(X0,X1,sK6(X1)),X1)
| sP2(X0,X1,sK6(X1))
| empty(X1) )
| ~ spl22_370 ),
inference(factoring,[],[f4153]) ).
fof(f16485,plain,
( spl22_896
| ~ spl22_368 ),
inference(avatar_split_clause,[],[f4347,f4144,f16483]) ).
fof(f16483,plain,
( spl22_896
<=> ! [X0,X1] :
( element(sK13(X0,sK6(X1),X1),X1)
| sP2(X0,sK6(X1),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_896])]) ).
fof(f4347,plain,
( ! [X0,X1] :
( element(sK13(X0,sK6(X1),X1),X1)
| sP2(X0,sK6(X1),X1)
| empty(X1) )
| ~ spl22_368 ),
inference(factoring,[],[f4145]) ).
fof(f16481,plain,
( spl22_895
| ~ spl22_250
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3533,f3327,f2571,f16479]) ).
fof(f16479,plain,
( spl22_895
<=> ! [X31,X34,X33,X32] :
( ~ empty(X31)
| sP2(sK10(powerset(X31)),X32,relation_dom(X33))
| ~ sP0(X33,X34)
| ~ empty(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_895])]) ).
fof(f3533,plain,
( ! [X31,X34,X32,X33] :
( ~ empty(X31)
| sP2(sK10(powerset(X31)),X32,relation_dom(X33))
| ~ sP0(X33,X34)
| ~ empty(X34) )
| ~ spl22_250
| ~ spl22_315 ),
inference(resolution,[],[f3328,f2572]) ).
fof(f16477,plain,
( spl22_894
| ~ spl22_250
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3516,f3323,f2571,f16475]) ).
fof(f16475,plain,
( spl22_894
<=> ! [X31,X34,X33,X32] :
( ~ empty(X31)
| sP2(X32,sK10(powerset(X31)),relation_dom(X33))
| ~ sP0(X33,X34)
| ~ empty(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_894])]) ).
fof(f3516,plain,
( ! [X31,X34,X32,X33] :
( ~ empty(X31)
| sP2(X32,sK10(powerset(X31)),relation_dom(X33))
| ~ sP0(X33,X34)
| ~ empty(X34) )
| ~ spl22_250
| ~ spl22_314 ),
inference(resolution,[],[f3324,f2572]) ).
fof(f16473,plain,
( spl22_893
| ~ spl22_250
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3499,f3319,f2571,f16471]) ).
fof(f16471,plain,
( spl22_893
<=> ! [X31,X33,X32,X30] :
( ~ empty(X30)
| sP2(X31,relation_dom(X32),sK10(powerset(X30)))
| ~ sP0(X32,X33)
| ~ empty(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_893])]) ).
fof(f3499,plain,
( ! [X31,X32,X30,X33] :
( ~ empty(X30)
| sP2(X31,relation_dom(X32),sK10(powerset(X30)))
| ~ sP0(X32,X33)
| ~ empty(X33) )
| ~ spl22_250
| ~ spl22_313 ),
inference(resolution,[],[f3320,f2572]) ).
fof(f16469,plain,
( spl22_892
| ~ spl22_250
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3465,f3315,f2571,f16467]) ).
fof(f16467,plain,
( spl22_892
<=> ! [X31,X33,X32,X30] :
( ~ empty(X30)
| sP2(relation_dom(X31),X32,sK10(powerset(X30)))
| ~ sP0(X31,X33)
| ~ empty(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_892])]) ).
fof(f3465,plain,
( ! [X31,X32,X30,X33] :
( ~ empty(X30)
| sP2(relation_dom(X31),X32,sK10(powerset(X30)))
| ~ sP0(X31,X33)
| ~ empty(X33) )
| ~ spl22_250
| ~ spl22_312 ),
inference(resolution,[],[f3316,f2572]) ).
fof(f16465,plain,
( spl22_891
| ~ spl22_197
| ~ spl22_310 ),
inference(avatar_split_clause,[],[f3313,f3272,f1926,f16463]) ).
fof(f16463,plain,
( spl22_891
<=> ! [X0] :
( element(sK8(sK15,sK10(powerset(X0))),sK15)
| sP0(sK15,sK10(powerset(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_891])]) ).
fof(f3272,plain,
( spl22_310
<=> ! [X13,X14] :
( element(sK8(X13,sK10(powerset(X14))),relation_dom(X13))
| sP0(X13,sK10(powerset(X14)))
| ~ empty(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_310])]) ).
fof(f3313,plain,
( ! [X0] :
( element(sK8(sK15,sK10(powerset(X0))),sK15)
| sP0(sK15,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_197
| ~ spl22_310 ),
inference(superposition,[],[f3273,f1928]) ).
fof(f3273,plain,
( ! [X14,X13] :
( element(sK8(X13,sK10(powerset(X14))),relation_dom(X13))
| sP0(X13,sK10(powerset(X14)))
| ~ empty(X14) )
| ~ spl22_310 ),
inference(avatar_component_clause,[],[f3272]) ).
fof(f16461,plain,
( spl22_890
| ~ spl22_197
| ~ spl22_306 ),
inference(avatar_split_clause,[],[f3282,f3256,f1926,f16459]) ).
fof(f16459,plain,
( spl22_890
<=> ! [X0] :
( in(sK8(sK15,sK10(powerset(X0))),sK15)
| ~ empty(X0)
| sP0(sK15,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_890])]) ).
fof(f3282,plain,
( ! [X0] :
( in(sK8(sK15,sK10(powerset(X0))),sK15)
| ~ empty(X0)
| sP0(sK15,sK10(powerset(X0))) )
| ~ spl22_197
| ~ spl22_306 ),
inference(superposition,[],[f3257,f1928]) ).
fof(f16457,plain,
( ~ spl22_889
| ~ spl22_45
| ~ spl22_840 ),
inference(avatar_split_clause,[],[f16225,f15376,f448,f16454]) ).
fof(f16454,plain,
( spl22_889
<=> in(set_intersection2(sK3,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_889])]) ).
fof(f16225,plain,
( ~ in(set_intersection2(sK3,relation_dom(sK5)),sK4)
| ~ spl22_45
| ~ spl22_840 ),
inference(resolution,[],[f15377,f449]) ).
fof(f16452,plain,
( spl22_888
| ~ spl22_52
| ~ spl22_295 ),
inference(avatar_split_clause,[],[f3168,f3067,f498,f16450]) ).
fof(f16450,plain,
( spl22_888
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_888])]) ).
fof(f3168,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_295 ),
inference(resolution,[],[f3068,f499]) ).
fof(f16448,plain,
( spl22_887
| ~ spl22_52
| ~ spl22_293 ),
inference(avatar_split_clause,[],[f3163,f3059,f498,f16446]) ).
fof(f16446,plain,
( spl22_887
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(powerset(X9),X10,X8)
| subset(sK13(powerset(X9),X10,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_887])]) ).
fof(f3163,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(powerset(X9),X10,X8)
| subset(sK13(powerset(X9),X10,X8),X9) )
| ~ spl22_52
| ~ spl22_293 ),
inference(resolution,[],[f3060,f499]) ).
fof(f16444,plain,
( spl22_886
| ~ spl22_52
| ~ spl22_291 ),
inference(avatar_split_clause,[],[f3158,f3051,f498,f16442]) ).
fof(f16442,plain,
( spl22_886
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X9,X8,powerset(X10))
| subset(sK13(X9,X8,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_886])]) ).
fof(f3158,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X9,X8,powerset(X10))
| subset(sK13(X9,X8,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_291 ),
inference(resolution,[],[f3052,f499]) ).
fof(f16440,plain,
( spl22_885
| ~ spl22_52
| ~ spl22_289 ),
inference(avatar_split_clause,[],[f3153,f3031,f498,f16438]) ).
fof(f16438,plain,
( spl22_885
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| sP2(X9,powerset(X10),X8)
| subset(sK13(X9,powerset(X10),X8),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_885])]) ).
fof(f3153,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| sP2(X9,powerset(X10),X8)
| subset(sK13(X9,powerset(X10),X8),X10) )
| ~ spl22_52
| ~ spl22_289 ),
inference(resolution,[],[f3032,f499]) ).
fof(f16436,plain,
( spl22_884
| ~ spl22_37
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2937,f2799,f397,f16434]) ).
fof(f16434,plain,
( spl22_884
<=> ! [X3] :
( ~ function(relation_dom(X3))
| relation_dom(X3) = relation_dom_restriction(relation_dom(X3),relation_dom(relation_dom(X3)))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_884])]) ).
fof(f2937,plain,
( ! [X3] :
( ~ function(relation_dom(X3))
| relation_dom(X3) = relation_dom_restriction(relation_dom(X3),relation_dom(relation_dom(X3)))
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_276 ),
inference(resolution,[],[f2800,f398]) ).
fof(f16432,plain,
( spl22_883
| ~ spl22_35
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2936,f2799,f389,f16430]) ).
fof(f16430,plain,
( spl22_883
<=> ! [X2] :
( ~ function(relation_rng(X2))
| relation_rng(X2) = relation_dom_restriction(relation_rng(X2),relation_dom(relation_rng(X2)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_883])]) ).
fof(f2936,plain,
( ! [X2] :
( ~ function(relation_rng(X2))
| relation_rng(X2) = relation_dom_restriction(relation_rng(X2),relation_dom(relation_rng(X2)))
| ~ empty(X2) )
| ~ spl22_35
| ~ spl22_276 ),
inference(resolution,[],[f2800,f390]) ).
fof(f16428,plain,
( spl22_882
| ~ spl22_65
| ~ spl22_275 ),
inference(avatar_split_clause,[],[f2931,f2795,f610,f16426]) ).
fof(f16426,plain,
( spl22_882
<=> ! [X2,X0,X1] :
( sP2(powerset(X0),X1,sK15)
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_882])]) ).
fof(f2931,plain,
( ! [X2,X0,X1] :
( sP2(powerset(X0),X1,sK15)
| ~ empty(X0)
| ~ in(X2,sK13(powerset(X0),X1,sK15)) )
| ~ spl22_65
| ~ spl22_275 ),
inference(resolution,[],[f2796,f611]) ).
fof(f16424,plain,
( spl22_881
| ~ spl22_65
| ~ spl22_274 ),
inference(avatar_split_clause,[],[f2924,f2791,f610,f16422]) ).
fof(f16422,plain,
( spl22_881
<=> ! [X2,X0,X1] :
( sP2(sK15,X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(sK15,X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_881])]) ).
fof(f2924,plain,
( ! [X2,X0,X1] :
( sP2(sK15,X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(sK15,X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_274 ),
inference(resolution,[],[f2792,f611]) ).
fof(f16420,plain,
( spl22_880
| ~ spl22_65
| ~ spl22_273 ),
inference(avatar_split_clause,[],[f2920,f2787,f610,f16418]) ).
fof(f16418,plain,
( spl22_880
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1),sK15)
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_880])]) ).
fof(f2920,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1),sK15)
| ~ empty(X1)
| ~ in(X2,sK13(X0,powerset(X1),sK15)) )
| ~ spl22_65
| ~ spl22_273 ),
inference(resolution,[],[f2788,f611]) ).
fof(f16416,plain,
( spl22_879
| ~ spl22_65
| ~ spl22_272 ),
inference(avatar_split_clause,[],[f2916,f2783,f610,f16414]) ).
fof(f16414,plain,
( spl22_879
<=> ! [X2,X0,X1] :
( sP2(X0,sK15,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK15,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_879])]) ).
fof(f2916,plain,
( ! [X2,X0,X1] :
( sP2(X0,sK15,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK13(X0,sK15,powerset(X1))) )
| ~ spl22_65
| ~ spl22_272 ),
inference(resolution,[],[f2784,f611]) ).
fof(f16412,plain,
( spl22_878
| ~ spl22_46
| ~ spl22_840 ),
inference(avatar_split_clause,[],[f16224,f15376,f452,f16409]) ).
fof(f16409,plain,
( spl22_878
<=> element(sK4,set_intersection2(sK3,relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_878])]) ).
fof(f16224,plain,
( element(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_46
| ~ spl22_840 ),
inference(resolution,[],[f15377,f453]) ).
fof(f16407,plain,
( spl22_877
| ~ spl22_52
| ~ spl22_264 ),
inference(avatar_split_clause,[],[f2888,f2747,f498,f16405]) ).
fof(f16405,plain,
( spl22_877
<=> ! [X6,X7] :
( sP2(powerset(X6),X7,powerset(X6))
| subset(sK13(powerset(X6),X7,powerset(X6)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_877])]) ).
fof(f2888,plain,
( ! [X6,X7] :
( sP2(powerset(X6),X7,powerset(X6))
| subset(sK13(powerset(X6),X7,powerset(X6)),X6) )
| ~ spl22_52
| ~ spl22_264 ),
inference(resolution,[],[f2748,f499]) ).
fof(f16403,plain,
( spl22_876
| ~ spl22_52
| ~ spl22_261 ),
inference(avatar_split_clause,[],[f2879,f2735,f498,f16401]) ).
fof(f16401,plain,
( spl22_876
<=> ! [X6,X7] :
( sP2(X6,powerset(X7),powerset(X7))
| subset(sK13(X6,powerset(X7),powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_876])]) ).
fof(f2879,plain,
( ! [X6,X7] :
( sP2(X6,powerset(X7),powerset(X7))
| subset(sK13(X6,powerset(X7),powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_261 ),
inference(resolution,[],[f2736,f499]) ).
fof(f16399,plain,
( spl22_875
| ~ spl22_143
| ~ spl22_259 ),
inference(avatar_split_clause,[],[f2876,f2727,f1304,f16397]) ).
fof(f16397,plain,
( spl22_875
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_875])]) ).
fof(f2876,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl22_143
| ~ spl22_259 ),
inference(resolution,[],[f2728,f1305]) ).
fof(f16395,plain,
( spl22_874
| ~ spl22_65
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2867,f2715,f610,f16393]) ).
fof(f16393,plain,
( spl22_874
<=> ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_874])]) ).
fof(f2867,plain,
( ! [X0,X1] :
( empty(sK10(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK10(sK10(powerset(powerset(X0))))) )
| ~ spl22_65
| ~ spl22_256 ),
inference(resolution,[],[f2716,f611]) ).
fof(f16391,plain,
( spl22_873
| ~ spl22_137
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2863,f2711,f1213,f16389]) ).
fof(f16389,plain,
( spl22_873
<=> ! [X27,X28] :
( sP2(sK15,X27,sK10(powerset(X28)))
| element(sK13(sK15,X27,sK10(powerset(X28))),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_873])]) ).
fof(f2863,plain,
( ! [X28,X27] :
( sP2(sK15,X27,sK10(powerset(X28)))
| element(sK13(sK15,X27,sK10(powerset(X28))),X28) )
| ~ spl22_137
| ~ spl22_255 ),
inference(resolution,[],[f2712,f1214]) ).
fof(f16387,plain,
( spl22_872
| ~ spl22_141
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2862,f2711,f1277,f16385]) ).
fof(f16385,plain,
( spl22_872
<=> ! [X25,X26] :
( sP2(sK15,X25,sK6(X26))
| element(sK13(sK15,X25,sK6(X26)),X26)
| empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_872])]) ).
fof(f2862,plain,
( ! [X26,X25] :
( sP2(sK15,X25,sK6(X26))
| element(sK13(sK15,X25,sK6(X26)),X26)
| empty(X26) )
| ~ spl22_141
| ~ spl22_255 ),
inference(resolution,[],[f2712,f1278]) ).
fof(f16383,plain,
( spl22_871
| ~ spl22_237
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2858,f2711,f2435,f16381]) ).
fof(f16381,plain,
( spl22_871
<=> ! [X16,X14,X15] :
( sP2(sK15,X14,set_intersection2(X15,X16))
| in(sK13(sK15,X14,set_intersection2(X15,X16)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_871])]) ).
fof(f2858,plain,
( ! [X16,X14,X15] :
( sP2(sK15,X14,set_intersection2(X15,X16))
| in(sK13(sK15,X14,set_intersection2(X15,X16)),X16) )
| ~ spl22_237
| ~ spl22_255 ),
inference(resolution,[],[f2712,f2436]) ).
fof(f16379,plain,
( spl22_870
| ~ spl22_238
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2857,f2711,f2439,f16377]) ).
fof(f16377,plain,
( spl22_870
<=> ! [X13,X12,X11] :
( sP2(sK15,X11,set_intersection2(X12,X13))
| in(sK13(sK15,X11,set_intersection2(X12,X13)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_870])]) ).
fof(f2857,plain,
( ! [X11,X12,X13] :
( sP2(sK15,X11,set_intersection2(X12,X13))
| in(sK13(sK15,X11,set_intersection2(X12,X13)),X12) )
| ~ spl22_238
| ~ spl22_255 ),
inference(resolution,[],[f2712,f2440]) ).
fof(f16375,plain,
( spl22_869
| ~ spl22_137
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2848,f2707,f1213,f16373]) ).
fof(f16373,plain,
( spl22_869
<=> ! [X27,X28] :
( sP2(X27,sK15,sK10(powerset(X28)))
| element(sK13(X27,sK15,sK10(powerset(X28))),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_869])]) ).
fof(f2848,plain,
( ! [X28,X27] :
( sP2(X27,sK15,sK10(powerset(X28)))
| element(sK13(X27,sK15,sK10(powerset(X28))),X28) )
| ~ spl22_137
| ~ spl22_254 ),
inference(resolution,[],[f2708,f1214]) ).
fof(f16371,plain,
( spl22_868
| ~ spl22_141
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2847,f2707,f1277,f16369]) ).
fof(f16369,plain,
( spl22_868
<=> ! [X25,X26] :
( sP2(X25,sK15,sK6(X26))
| element(sK13(X25,sK15,sK6(X26)),X26)
| empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_868])]) ).
fof(f2847,plain,
( ! [X26,X25] :
( sP2(X25,sK15,sK6(X26))
| element(sK13(X25,sK15,sK6(X26)),X26)
| empty(X26) )
| ~ spl22_141
| ~ spl22_254 ),
inference(resolution,[],[f2708,f1278]) ).
fof(f16366,plain,
( spl22_867
| ~ spl22_237
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2843,f2707,f2435,f16364]) ).
fof(f16364,plain,
( spl22_867
<=> ! [X16,X14,X15] :
( sP2(X14,sK15,set_intersection2(X15,X16))
| in(sK13(X14,sK15,set_intersection2(X15,X16)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_867])]) ).
fof(f2843,plain,
( ! [X16,X14,X15] :
( sP2(X14,sK15,set_intersection2(X15,X16))
| in(sK13(X14,sK15,set_intersection2(X15,X16)),X16) )
| ~ spl22_237
| ~ spl22_254 ),
inference(resolution,[],[f2708,f2436]) ).
fof(f16362,plain,
( spl22_866
| ~ spl22_238
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2842,f2707,f2439,f16360]) ).
fof(f16360,plain,
( spl22_866
<=> ! [X13,X12,X11] :
( sP2(X11,sK15,set_intersection2(X12,X13))
| in(sK13(X11,sK15,set_intersection2(X12,X13)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_866])]) ).
fof(f2842,plain,
( ! [X11,X12,X13] :
( sP2(X11,sK15,set_intersection2(X12,X13))
| in(sK13(X11,sK15,set_intersection2(X12,X13)),X12) )
| ~ spl22_238
| ~ spl22_254 ),
inference(resolution,[],[f2708,f2440]) ).
fof(f16358,plain,
( spl22_865
| ~ spl22_137
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2828,f2703,f1213,f16356]) ).
fof(f16356,plain,
( spl22_865
<=> ! [X27,X26] :
( sP2(X26,sK10(powerset(X27)),sK15)
| element(sK13(X26,sK10(powerset(X27)),sK15),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_865])]) ).
fof(f2828,plain,
( ! [X26,X27] :
( sP2(X26,sK10(powerset(X27)),sK15)
| element(sK13(X26,sK10(powerset(X27)),sK15),X27) )
| ~ spl22_137
| ~ spl22_253 ),
inference(resolution,[],[f2704,f1214]) ).
fof(f16354,plain,
( spl22_864
| ~ spl22_141
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2827,f2703,f1277,f16352]) ).
fof(f16352,plain,
( spl22_864
<=> ! [X25,X24] :
( sP2(X24,sK6(X25),sK15)
| element(sK13(X24,sK6(X25),sK15),X25)
| empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_864])]) ).
fof(f2827,plain,
( ! [X24,X25] :
( sP2(X24,sK6(X25),sK15)
| element(sK13(X24,sK6(X25),sK15),X25)
| empty(X25) )
| ~ spl22_141
| ~ spl22_253 ),
inference(resolution,[],[f2704,f1278]) ).
fof(f16350,plain,
( spl22_863
| ~ spl22_237
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2823,f2703,f2435,f16348]) ).
fof(f16348,plain,
( spl22_863
<=> ! [X13,X14,X15] :
( sP2(X13,set_intersection2(X14,X15),sK15)
| in(sK13(X13,set_intersection2(X14,X15),sK15),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_863])]) ).
fof(f2823,plain,
( ! [X14,X15,X13] :
( sP2(X13,set_intersection2(X14,X15),sK15)
| in(sK13(X13,set_intersection2(X14,X15),sK15),X15) )
| ~ spl22_237
| ~ spl22_253 ),
inference(resolution,[],[f2704,f2436]) ).
fof(f16346,plain,
( spl22_862
| ~ spl22_238
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2822,f2703,f2439,f16344]) ).
fof(f16344,plain,
( spl22_862
<=> ! [X11,X12,X10] :
( sP2(X10,set_intersection2(X11,X12),sK15)
| in(sK13(X10,set_intersection2(X11,X12),sK15),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_862])]) ).
fof(f2822,plain,
( ! [X10,X11,X12] :
( sP2(X10,set_intersection2(X11,X12),sK15)
| in(sK13(X10,set_intersection2(X11,X12),sK15),X11) )
| ~ spl22_238
| ~ spl22_253 ),
inference(resolution,[],[f2704,f2440]) ).
fof(f16342,plain,
( spl22_861
| ~ spl22_137
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2813,f2699,f1213,f16340]) ).
fof(f16340,plain,
( spl22_861
<=> ! [X27,X26] :
( sP2(sK10(powerset(X26)),X27,sK15)
| element(sK13(sK10(powerset(X26)),X27,sK15),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_861])]) ).
fof(f2813,plain,
( ! [X26,X27] :
( sP2(sK10(powerset(X26)),X27,sK15)
| element(sK13(sK10(powerset(X26)),X27,sK15),X26) )
| ~ spl22_137
| ~ spl22_252 ),
inference(resolution,[],[f2700,f1214]) ).
fof(f16327,plain,
( spl22_860
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_440
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16017,f15007,f6151,f1062,f494,f15376,f16325]) ).
fof(f16325,plain,
( spl22_860
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_860])]) ).
fof(f1062,plain,
( spl22_117
<=> apply(sK5,sK4) = apply(relation_dom_restriction(sK5,sK3),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_117])]) ).
fof(f16017,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_440
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16016,f495]) ).
fof(f16016,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_440
| ~ spl22_823 ),
inference(forward_demodulation,[],[f6251,f15008]) ).
fof(f6251,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sK7(X0,apply(sK5,sK4)) = apply(X0,sK8(X0,apply(sK5,sK4)))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_440 ),
inference(superposition,[],[f6152,f1064]) ).
fof(f1064,plain,
( apply(sK5,sK4) = apply(relation_dom_restriction(sK5,sK3),sK4)
| ~ spl22_117 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f16305,plain,
( ~ spl22_859
| ~ spl22_41
| ~ spl22_840 ),
inference(avatar_split_clause,[],[f16222,f15376,f414,f16302]) ).
fof(f16302,plain,
( spl22_859
<=> empty(set_intersection2(sK3,relation_dom(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_859])]) ).
fof(f16222,plain,
( ~ empty(set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_41
| ~ spl22_840 ),
inference(resolution,[],[f15377,f415]) ).
fof(f16300,plain,
( spl22_858
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_417
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16015,f15007,f5478,f1062,f494,f15376,f16298]) ).
fof(f16298,plain,
( spl22_858
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| sP2(apply(sK5,sK4),X0,X1)
| in(sK13(apply(sK5,sK4),X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_858])]) ).
fof(f16015,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| in(sK13(apply(sK5,sK4),X0,X1),X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_417
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16014,f495]) ).
fof(f16014,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| in(sK13(apply(sK5,sK4),X0,X1),X1)
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_117
| ~ spl22_417
| ~ spl22_823 ),
inference(forward_demodulation,[],[f5554,f15008]) ).
fof(f5554,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(apply(sK5,sK4),X0,X1))
| in(sK13(apply(sK5,sK4),X0,X1),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP2(apply(sK5,sK4),X0,X1) )
| ~ spl22_117
| ~ spl22_417 ),
inference(superposition,[],[f5479,f1064]) ).
fof(f16283,plain,
( spl22_857
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_416
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16013,f15007,f5474,f1062,f494,f15376,f16281]) ).
fof(f16281,plain,
( spl22_857
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| in(sK13(X0,X1,apply(sK5,sK4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_857])]) ).
fof(f16013,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_416
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16012,f495]) ).
fof(f16012,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X0)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_416
| ~ spl22_823 ),
inference(forward_demodulation,[],[f5541,f15008]) ).
fof(f5541,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_416 ),
inference(superposition,[],[f5475,f1064]) ).
fof(f16261,plain,
( spl22_856
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_415
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16011,f15007,f5466,f1062,f494,f15376,f16259]) ).
fof(f16259,plain,
( spl22_856
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| sP2(X0,apply(sK5,sK4),X1)
| in(sK13(X0,apply(sK5,sK4),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_856])]) ).
fof(f16011,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| in(sK13(X0,apply(sK5,sK4),X1),X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_415
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16010,f495]) ).
fof(f16010,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| in(sK13(X0,apply(sK5,sK4),X1),X1)
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_117
| ~ spl22_415
| ~ spl22_823 ),
inference(forward_demodulation,[],[f5528,f15008]) ).
fof(f5528,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,apply(sK5,sK4),X1))
| in(sK13(X0,apply(sK5,sK4),X1),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP2(X0,apply(sK5,sK4),X1) )
| ~ spl22_117
| ~ spl22_415 ),
inference(superposition,[],[f5467,f1064]) ).
fof(f16244,plain,
( spl22_855
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_414
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16009,f15007,f5462,f1062,f494,f15376,f16242]) ).
fof(f16242,plain,
( spl22_855
<=> ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| sP2(X0,X1,apply(sK5,sK4))
| in(sK13(X0,X1,apply(sK5,sK4)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_855])]) ).
fof(f16009,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_414
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16008,f495]) ).
fof(f16008,plain,
( ! [X0,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X1)
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_414
| ~ spl22_823 ),
inference(forward_demodulation,[],[f5515,f15008]) ).
fof(f5515,plain,
( ! [X0,X1] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK13(X0,X1,apply(sK5,sK4)))
| in(sK13(X0,X1,apply(sK5,sK4)),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP2(X0,X1,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_414 ),
inference(superposition,[],[f5463,f1064]) ).
fof(f16229,plain,
( spl22_854
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_397
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16007,f15007,f5079,f1062,f494,f15376,f16227]) ).
fof(f16227,plain,
( spl22_854
<=> ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| sP0(X0,apply(sK5,sK4))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_854])]) ).
fof(f16007,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_397
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16006,f495]) ).
fof(f16006,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_397
| ~ spl22_823 ),
inference(forward_demodulation,[],[f5289,f15008]) ).
fof(f5289,plain,
( ! [X0] :
( ~ sP0(relation_dom_restriction(sK5,sK3),sK7(X0,apply(sK5,sK4)))
| in(sK8(X0,apply(sK5,sK4)),relation_dom(X0))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| sP0(X0,apply(sK5,sK4)) )
| ~ spl22_117
| ~ spl22_397 ),
inference(superposition,[],[f5080,f1064]) ).
fof(f16217,plain,
( spl22_853
| ~ spl22_840
| ~ spl22_51
| ~ spl22_80
| ~ spl22_117
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15999,f15007,f1062,f726,f494,f15376,f16215]) ).
fof(f16215,plain,
( spl22_853
<=> ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| ~ in(apply(sK5,sK4),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_853])]) ).
fof(f726,plain,
( spl22_80
<=> ! [X0,X1,X3] :
( sP0(X0,X1)
| apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_80])]) ).
fof(f15999,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(apply(sK5,sK4),X0) )
| ~ spl22_51
| ~ spl22_80
| ~ spl22_117
| ~ spl22_823 ),
inference(forward_demodulation,[],[f15998,f495]) ).
fof(f15998,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(apply(sK5,sK4),X0) )
| ~ spl22_80
| ~ spl22_117
| ~ spl22_823 ),
inference(forward_demodulation,[],[f1101,f15008]) ).
fof(f1101,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ in(apply(sK5,sK4),X0) )
| ~ spl22_80
| ~ spl22_117 ),
inference(inner_rewriting,[],[f1099]) ).
fof(f1099,plain,
( ! [X0] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,sK3),X0)
| sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ in(sK7(relation_dom_restriction(sK5,sK3),X0),X0) )
| ~ spl22_80
| ~ spl22_117 ),
inference(superposition,[],[f727,f1064]) ).
fof(f727,plain,
( ! [X3,X0,X1] :
( apply(X0,X3) != sK7(X0,X1)
| sP0(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK7(X0,X1),X1) )
| ~ spl22_80 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f16204,plain,
( spl22_852
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_309
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16005,f15007,f3268,f1062,f494,f15376,f16202]) ).
fof(f16202,plain,
( spl22_852
<=> ! [X0] :
( element(apply(sK5,sK4),X0)
| empty(X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_852])]) ).
fof(f16005,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),sK6(X0))
| empty(X0) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_309
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16004,f495]) ).
fof(f16004,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),sK6(X0))
| empty(X0) )
| ~ spl22_117
| ~ spl22_309
| ~ spl22_823 ),
inference(forward_demodulation,[],[f3300,f15008]) ).
fof(f3300,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),sK6(X0))
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| empty(X0) )
| ~ spl22_117
| ~ spl22_309 ),
inference(superposition,[],[f3269,f1064]) ).
fof(f16199,plain,
( spl22_851
| ~ spl22_840
| ~ spl22_51
| ~ spl22_75
| ~ spl22_117
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15997,f15007,f1062,f678,f494,f15376,f16197]) ).
fof(f16197,plain,
( spl22_851
<=> ! [X2,X1] :
( apply(sK5,sK4) != X1
| ~ sP0(relation_dom_restriction(sK5,sK3),X2)
| in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_851])]) ).
fof(f678,plain,
( spl22_75
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_75])]) ).
fof(f15997,plain,
( ! [X2,X1] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| apply(sK5,sK4) != X1
| in(X1,X2)
| ~ sP0(relation_dom_restriction(sK5,sK3),X2) )
| ~ spl22_51
| ~ spl22_75
| ~ spl22_117
| ~ spl22_823 ),
inference(forward_demodulation,[],[f15996,f495]) ).
fof(f15996,plain,
( ! [X2,X1] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| apply(sK5,sK4) != X1
| in(X1,X2)
| ~ sP0(relation_dom_restriction(sK5,sK3),X2) )
| ~ spl22_75
| ~ spl22_117
| ~ spl22_823 ),
inference(forward_demodulation,[],[f1100,f15008]) ).
fof(f1100,plain,
( ! [X2,X1] :
( apply(sK5,sK4) != X1
| in(X1,X2)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ sP0(relation_dom_restriction(sK5,sK3),X2) )
| ~ spl22_75
| ~ spl22_117 ),
inference(superposition,[],[f679,f1064]) ).
fof(f679,plain,
( ! [X0,X1,X6,X5] :
( apply(X0,X6) != X5
| in(X5,X1)
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) )
| ~ spl22_75 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f16139,plain,
( spl22_850
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_288
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16003,f15007,f3027,f1062,f494,f15376,f16137]) ).
fof(f16137,plain,
( spl22_850
<=> ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_850])]) ).
fof(f16003,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_288
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16002,f495]) ).
fof(f16002,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) )
| ~ spl22_117
| ~ spl22_288
| ~ spl22_823 ),
inference(forward_demodulation,[],[f3140,f15008]) ).
fof(f3140,plain,
( ! [X0] :
( ~ in(X0,apply(sK5,sK4))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_117
| ~ spl22_288 ),
inference(superposition,[],[f3028,f1064]) ).
fof(f16079,plain,
( spl22_849
| ~ spl22_840
| ~ spl22_51
| ~ spl22_117
| ~ spl22_287
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f16001,f15007,f3023,f1062,f494,f15376,f16077]) ).
fof(f16077,plain,
( spl22_849
<=> ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_849])]) ).
fof(f16001,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) )
| ~ spl22_51
| ~ spl22_117
| ~ spl22_287
| ~ spl22_823 ),
inference(forward_demodulation,[],[f16000,f495]) ).
fof(f16000,plain,
( ! [X0] :
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) )
| ~ spl22_117
| ~ spl22_287
| ~ spl22_823 ),
inference(forward_demodulation,[],[f3096,f15008]) ).
fof(f3096,plain,
( ! [X0] :
( element(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,sK3),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) )
| ~ spl22_117
| ~ spl22_287 ),
inference(superposition,[],[f3024,f1064]) ).
fof(f15981,plain,
( ~ spl22_4
| ~ spl22_3
| ~ spl22_278
| spl22_840 ),
inference(avatar_split_clause,[],[f15852,f15376,f2959,f229,f234]) ).
fof(f234,plain,
( spl22_4
<=> in(sK4,relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).
fof(f229,plain,
( spl22_3
<=> in(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).
fof(f15852,plain,
( ~ in(sK4,sK3)
| ~ in(sK4,relation_dom(sK5))
| ~ spl22_278
| spl22_840 ),
inference(resolution,[],[f15378,f2960]) ).
fof(f15378,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| spl22_840 ),
inference(avatar_component_clause,[],[f15376]) ).
fof(f15980,plain,
( spl22_848
| ~ spl22_141
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2812,f2699,f1277,f15978]) ).
fof(f15978,plain,
( spl22_848
<=> ! [X25,X24] :
( sP2(sK6(X24),X25,sK15)
| element(sK13(sK6(X24),X25,sK15),X24)
| empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_848])]) ).
fof(f2812,plain,
( ! [X24,X25] :
( sP2(sK6(X24),X25,sK15)
| element(sK13(sK6(X24),X25,sK15),X24)
| empty(X24) )
| ~ spl22_141
| ~ spl22_252 ),
inference(resolution,[],[f2700,f1278]) ).
fof(f15976,plain,
( spl22_847
| ~ spl22_237
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2808,f2699,f2435,f15974]) ).
fof(f15974,plain,
( spl22_847
<=> ! [X13,X14,X15] :
( sP2(set_intersection2(X13,X14),X15,sK15)
| in(sK13(set_intersection2(X13,X14),X15,sK15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_847])]) ).
fof(f2808,plain,
( ! [X14,X15,X13] :
( sP2(set_intersection2(X13,X14),X15,sK15)
| in(sK13(set_intersection2(X13,X14),X15,sK15),X14) )
| ~ spl22_237
| ~ spl22_252 ),
inference(resolution,[],[f2700,f2436]) ).
fof(f15972,plain,
( spl22_846
| ~ spl22_238
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2807,f2699,f2439,f15970]) ).
fof(f15970,plain,
( spl22_846
<=> ! [X11,X12,X10] :
( sP2(set_intersection2(X10,X11),X12,sK15)
| in(sK13(set_intersection2(X10,X11),X12,sK15),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_846])]) ).
fof(f2807,plain,
( ! [X10,X11,X12] :
( sP2(set_intersection2(X10,X11),X12,sK15)
| in(sK13(set_intersection2(X10,X11),X12,sK15),X10) )
| ~ spl22_238
| ~ spl22_252 ),
inference(resolution,[],[f2700,f2440]) ).
fof(f15968,plain,
( spl22_845
| ~ spl22_153
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2502,f2439,f1395,f15966]) ).
fof(f15966,plain,
( spl22_845
<=> ! [X0,X3,X2,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_845])]) ).
fof(f2502,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X2,X3)) )
| ~ spl22_153
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1396]) ).
fof(f15964,plain,
( spl22_844
| ~ spl22_153
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2471,f2435,f1395,f15962]) ).
fof(f15962,plain,
( spl22_844
<=> ! [X0,X3,X2,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_844])]) ).
fof(f2471,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,set_intersection2(X3,X2)) )
| ~ spl22_153
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1396]) ).
fof(f15960,plain,
( spl22_843
| ~ spl22_74
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2409,f2331,f668,f15958]) ).
fof(f15958,plain,
( spl22_843
<=> ! [X12,X11] :
( ~ sP0(X11,sK15)
| in(sK8(X12,relation_dom(X11)),relation_dom(X12))
| sP0(X12,relation_dom(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_843])]) ).
fof(f2409,plain,
( ! [X11,X12] :
( ~ sP0(X11,sK15)
| in(sK8(X12,relation_dom(X11)),relation_dom(X12))
| sP0(X12,relation_dom(X11)) )
| ~ spl22_74
| ~ spl22_236 ),
inference(resolution,[],[f2332,f669]) ).
fof(f15956,plain,
( spl22_842
| ~ spl22_159
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2406,f2331,f1481,f15954]) ).
fof(f15954,plain,
( spl22_842
<=> ! [X6,X5] :
( ~ sP0(X5,sK15)
| element(sK8(X6,relation_dom(X5)),relation_dom(X6))
| sP0(X6,relation_dom(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_842])]) ).
fof(f2406,plain,
( ! [X6,X5] :
( ~ sP0(X5,sK15)
| element(sK8(X6,relation_dom(X5)),relation_dom(X6))
| sP0(X6,relation_dom(X5)) )
| ~ spl22_159
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1482]) ).
fof(f15952,plain,
( spl22_841
| ~ spl22_153
| ~ spl22_214 ),
inference(avatar_split_clause,[],[f2167,f2112,f1395,f15950]) ).
fof(f15950,plain,
( spl22_841
<=> ! [X0,X1] :
( empty(apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK10(apply(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_841])]) ).
fof(f2112,plain,
( spl22_214
<=> ! [X4] :
( empty(X4)
| ~ in(X4,sK10(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_214])]) ).
fof(f2167,plain,
( ! [X0,X1] :
( empty(apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK10(apply(X0,X1))) )
| ~ spl22_153
| ~ spl22_214 ),
inference(resolution,[],[f2113,f1396]) ).
fof(f2113,plain,
( ! [X4] :
( ~ in(X4,sK10(X4))
| empty(X4) )
| ~ spl22_214 ),
inference(avatar_component_clause,[],[f2112]) ).
fof(f15379,plain,
( ~ spl22_840
| ~ spl22_51
| spl22_500
| ~ spl22_823 ),
inference(avatar_split_clause,[],[f15158,f15007,f6990,f494,f15376]) ).
fof(f6990,plain,
( spl22_500
<=> in(sK4,relation_dom(relation_dom_restriction(sK5,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_500])]) ).
fof(f15158,plain,
( ~ in(sK4,set_intersection2(sK3,relation_dom(sK5)))
| ~ spl22_51
| spl22_500
| ~ spl22_823 ),
inference(forward_demodulation,[],[f15051,f495]) ).
fof(f15051,plain,
( ~ in(sK4,set_intersection2(relation_dom(sK5),sK3))
| spl22_500
| ~ spl22_823 ),
inference(superposition,[],[f6992,f15008]) ).
fof(f6992,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| spl22_500 ),
inference(avatar_component_clause,[],[f6990]) ).
fof(f15182,plain,
( spl22_839
| ~ spl22_228
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4904,f4590,f2256,f15180]) ).
fof(f15180,plain,
( spl22_839
<=> ! [X102,X101,X100,X99,X103] :
( sP2(powerset(X99),X100,X101)
| element(sK13(sK13(powerset(X99),X100,X101),X102,X103),X99)
| in(sK13(powerset(X99),X100,X101),X101)
| sP2(sK13(powerset(X99),X100,X101),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(powerset(X99),X100,X101),X102,X103)) = apply(sK5,sK13(sK13(powerset(X99),X100,X101),X102,X103)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_839])]) ).
fof(f4590,plain,
( spl22_387
<=> ! [X5,X4,X7,X6] :
( in(sK13(powerset(X4),X5,X6),X6)
| sP2(powerset(X4),X5,X6)
| element(X7,X4)
| ~ in(X7,sK13(powerset(X4),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_387])]) ).
fof(f4904,plain,
( ! [X101,X99,X102,X103,X100] :
( sP2(powerset(X99),X100,X101)
| element(sK13(sK13(powerset(X99),X100,X101),X102,X103),X99)
| in(sK13(powerset(X99),X100,X101),X101)
| sP2(sK13(powerset(X99),X100,X101),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(powerset(X99),X100,X101),X102,X103)) = apply(sK5,sK13(sK13(powerset(X99),X100,X101),X102,X103)) )
| ~ spl22_228
| ~ spl22_387 ),
inference(resolution,[],[f4591,f2257]) ).
fof(f4591,plain,
( ! [X6,X7,X4,X5] :
( ~ in(X7,sK13(powerset(X4),X5,X6))
| sP2(powerset(X4),X5,X6)
| element(X7,X4)
| in(sK13(powerset(X4),X5,X6),X6) )
| ~ spl22_387 ),
inference(avatar_component_clause,[],[f4590]) ).
fof(f15178,plain,
( spl22_838
| ~ spl22_225
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4900,f4590,f2222,f15176]) ).
fof(f15176,plain,
( spl22_838
<=> ! [X79,X81,X82,X80,X83] :
( sP2(powerset(X79),X80,X81)
| element(sK13(X82,sK13(powerset(X79),X80,X81),X83),X79)
| in(sK13(powerset(X79),X80,X81),X81)
| sP2(X82,sK13(powerset(X79),X80,X81),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(powerset(X79),X80,X81),X83)) = apply(sK5,sK13(X82,sK13(powerset(X79),X80,X81),X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_838])]) ).
fof(f4900,plain,
( ! [X82,X83,X80,X81,X79] :
( sP2(powerset(X79),X80,X81)
| element(sK13(X82,sK13(powerset(X79),X80,X81),X83),X79)
| in(sK13(powerset(X79),X80,X81),X81)
| sP2(X82,sK13(powerset(X79),X80,X81),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(powerset(X79),X80,X81),X83)) = apply(sK5,sK13(X82,sK13(powerset(X79),X80,X81),X83)) )
| ~ spl22_225
| ~ spl22_387 ),
inference(resolution,[],[f4591,f2223]) ).
fof(f15174,plain,
( spl22_837
| ~ spl22_229
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4899,f4590,f2271,f15172]) ).
fof(f15172,plain,
( spl22_837
<=> ! [X77,X74,X75,X78,X76] :
( sP2(powerset(X74),X75,X76)
| element(sK13(X77,X78,sK13(powerset(X74),X75,X76)),X74)
| in(sK13(powerset(X74),X75,X76),X76)
| sP2(X77,X78,sK13(powerset(X74),X75,X76))
| apply(sK5,sK13(X77,X78,sK13(powerset(X74),X75,X76))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(powerset(X74),X75,X76))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_837])]) ).
fof(f4899,plain,
( ! [X78,X76,X77,X74,X75] :
( sP2(powerset(X74),X75,X76)
| element(sK13(X77,X78,sK13(powerset(X74),X75,X76)),X74)
| in(sK13(powerset(X74),X75,X76),X76)
| sP2(X77,X78,sK13(powerset(X74),X75,X76))
| apply(sK5,sK13(X77,X78,sK13(powerset(X74),X75,X76))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(powerset(X74),X75,X76))) )
| ~ spl22_229
| ~ spl22_387 ),
inference(resolution,[],[f4591,f2272]) ).
fof(f15170,plain,
( spl22_836
| ~ spl22_226
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4898,f4590,f2237,f15168]) ).
fof(f15168,plain,
( spl22_836
<=> ! [X69,X73,X71,X70,X72] :
( sP2(powerset(X69),X70,X71)
| element(sK13(X72,X73,sK13(powerset(X69),X70,X71)),X69)
| in(sK13(powerset(X69),X70,X71),X71)
| sP2(X72,X73,sK13(powerset(X69),X70,X71))
| apply(sK5,sK13(X72,X73,sK13(powerset(X69),X70,X71))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(powerset(X69),X70,X71))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_836])]) ).
fof(f4898,plain,
( ! [X72,X70,X73,X71,X69] :
( sP2(powerset(X69),X70,X71)
| element(sK13(X72,X73,sK13(powerset(X69),X70,X71)),X69)
| in(sK13(powerset(X69),X70,X71),X71)
| sP2(X72,X73,sK13(powerset(X69),X70,X71))
| apply(sK5,sK13(X72,X73,sK13(powerset(X69),X70,X71))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(powerset(X69),X70,X71))) )
| ~ spl22_226
| ~ spl22_387 ),
inference(resolution,[],[f4591,f2238]) ).
fof(f15166,plain,
( spl22_835
| ~ spl22_228
| ~ spl22_385 ),
inference(avatar_split_clause,[],[f4849,f4582,f2256,f15164]) ).
fof(f15164,plain,
( spl22_835
<=> ! [X102,X101,X100,X99,X103] :
( sP2(X99,X100,powerset(X101))
| element(sK13(sK13(X99,X100,powerset(X101)),X102,X103),X101)
| in(sK13(X99,X100,powerset(X101)),X99)
| sP2(sK13(X99,X100,powerset(X101)),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(X99,X100,powerset(X101)),X102,X103)) = apply(sK5,sK13(sK13(X99,X100,powerset(X101)),X102,X103)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_835])]) ).
fof(f4582,plain,
( spl22_385
<=> ! [X5,X4,X7,X6] :
( in(sK13(X4,X5,powerset(X6)),X4)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_385])]) ).
fof(f4849,plain,
( ! [X101,X99,X102,X103,X100] :
( sP2(X99,X100,powerset(X101))
| element(sK13(sK13(X99,X100,powerset(X101)),X102,X103),X101)
| in(sK13(X99,X100,powerset(X101)),X99)
| sP2(sK13(X99,X100,powerset(X101)),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(X99,X100,powerset(X101)),X102,X103)) = apply(sK5,sK13(sK13(X99,X100,powerset(X101)),X102,X103)) )
| ~ spl22_228
| ~ spl22_385 ),
inference(resolution,[],[f4583,f2257]) ).
fof(f4583,plain,
( ! [X6,X7,X4,X5] :
( ~ in(X7,sK13(X4,X5,powerset(X6)))
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| in(sK13(X4,X5,powerset(X6)),X4) )
| ~ spl22_385 ),
inference(avatar_component_clause,[],[f4582]) ).
fof(f15162,plain,
( spl22_834
| ~ spl22_225
| ~ spl22_385 ),
inference(avatar_split_clause,[],[f4845,f4582,f2222,f15160]) ).
fof(f15160,plain,
( spl22_834
<=> ! [X79,X81,X82,X80,X83] :
( sP2(X79,X80,powerset(X81))
| element(sK13(X82,sK13(X79,X80,powerset(X81)),X83),X81)
| in(sK13(X79,X80,powerset(X81)),X79)
| sP2(X82,sK13(X79,X80,powerset(X81)),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(X79,X80,powerset(X81)),X83)) = apply(sK5,sK13(X82,sK13(X79,X80,powerset(X81)),X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_834])]) ).
fof(f4845,plain,
( ! [X82,X83,X80,X81,X79] :
( sP2(X79,X80,powerset(X81))
| element(sK13(X82,sK13(X79,X80,powerset(X81)),X83),X81)
| in(sK13(X79,X80,powerset(X81)),X79)
| sP2(X82,sK13(X79,X80,powerset(X81)),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(X79,X80,powerset(X81)),X83)) = apply(sK5,sK13(X82,sK13(X79,X80,powerset(X81)),X83)) )
| ~ spl22_225
| ~ spl22_385 ),
inference(resolution,[],[f4583,f2223]) ).
fof(f15049,plain,
( spl22_833
| ~ spl22_229
| ~ spl22_385 ),
inference(avatar_split_clause,[],[f4844,f4582,f2271,f15047]) ).
fof(f15047,plain,
( spl22_833
<=> ! [X77,X74,X75,X78,X76] :
( sP2(X74,X75,powerset(X76))
| element(sK13(X77,X78,sK13(X74,X75,powerset(X76))),X76)
| in(sK13(X74,X75,powerset(X76)),X74)
| sP2(X77,X78,sK13(X74,X75,powerset(X76)))
| apply(sK5,sK13(X77,X78,sK13(X74,X75,powerset(X76)))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(X74,X75,powerset(X76)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_833])]) ).
fof(f4844,plain,
( ! [X78,X76,X77,X74,X75] :
( sP2(X74,X75,powerset(X76))
| element(sK13(X77,X78,sK13(X74,X75,powerset(X76))),X76)
| in(sK13(X74,X75,powerset(X76)),X74)
| sP2(X77,X78,sK13(X74,X75,powerset(X76)))
| apply(sK5,sK13(X77,X78,sK13(X74,X75,powerset(X76)))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(X74,X75,powerset(X76)))) )
| ~ spl22_229
| ~ spl22_385 ),
inference(resolution,[],[f4583,f2272]) ).
fof(f15045,plain,
( spl22_832
| ~ spl22_226
| ~ spl22_385 ),
inference(avatar_split_clause,[],[f4843,f4582,f2237,f15043]) ).
fof(f15043,plain,
( spl22_832
<=> ! [X69,X73,X71,X70,X72] :
( sP2(X69,X70,powerset(X71))
| element(sK13(X72,X73,sK13(X69,X70,powerset(X71))),X71)
| in(sK13(X69,X70,powerset(X71)),X69)
| sP2(X72,X73,sK13(X69,X70,powerset(X71)))
| apply(sK5,sK13(X72,X73,sK13(X69,X70,powerset(X71)))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(X69,X70,powerset(X71)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_832])]) ).
fof(f4843,plain,
( ! [X72,X70,X73,X71,X69] :
( sP2(X69,X70,powerset(X71))
| element(sK13(X72,X73,sK13(X69,X70,powerset(X71))),X71)
| in(sK13(X69,X70,powerset(X71)),X69)
| sP2(X72,X73,sK13(X69,X70,powerset(X71)))
| apply(sK5,sK13(X72,X73,sK13(X69,X70,powerset(X71)))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(X69,X70,powerset(X71)))) )
| ~ spl22_226
| ~ spl22_385 ),
inference(resolution,[],[f4583,f2238]) ).
fof(f15041,plain,
( spl22_831
| ~ spl22_228
| ~ spl22_382 ),
inference(avatar_split_clause,[],[f4794,f4570,f2256,f15039]) ).
fof(f15039,plain,
( spl22_831
<=> ! [X102,X101,X100,X99,X103] :
( sP2(X99,powerset(X100),X101)
| element(sK13(sK13(X99,powerset(X100),X101),X102,X103),X100)
| in(sK13(X99,powerset(X100),X101),X101)
| sP2(sK13(X99,powerset(X100),X101),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(X99,powerset(X100),X101),X102,X103)) = apply(sK5,sK13(sK13(X99,powerset(X100),X101),X102,X103)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_831])]) ).
fof(f4570,plain,
( spl22_382
<=> ! [X5,X4,X7,X6] :
( in(sK13(X4,powerset(X5),X6),X6)
| sP2(X4,powerset(X5),X6)
| element(X7,X5)
| ~ in(X7,sK13(X4,powerset(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_382])]) ).
fof(f4794,plain,
( ! [X101,X99,X102,X103,X100] :
( sP2(X99,powerset(X100),X101)
| element(sK13(sK13(X99,powerset(X100),X101),X102,X103),X100)
| in(sK13(X99,powerset(X100),X101),X101)
| sP2(sK13(X99,powerset(X100),X101),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(X99,powerset(X100),X101),X102,X103)) = apply(sK5,sK13(sK13(X99,powerset(X100),X101),X102,X103)) )
| ~ spl22_228
| ~ spl22_382 ),
inference(resolution,[],[f4571,f2257]) ).
fof(f4571,plain,
( ! [X6,X7,X4,X5] :
( ~ in(X7,sK13(X4,powerset(X5),X6))
| sP2(X4,powerset(X5),X6)
| element(X7,X5)
| in(sK13(X4,powerset(X5),X6),X6) )
| ~ spl22_382 ),
inference(avatar_component_clause,[],[f4570]) ).
fof(f15037,plain,
( spl22_830
| ~ spl22_225
| ~ spl22_382 ),
inference(avatar_split_clause,[],[f4790,f4570,f2222,f15035]) ).
fof(f15035,plain,
( spl22_830
<=> ! [X79,X81,X82,X80,X83] :
( sP2(X79,powerset(X80),X81)
| element(sK13(X82,sK13(X79,powerset(X80),X81),X83),X80)
| in(sK13(X79,powerset(X80),X81),X81)
| sP2(X82,sK13(X79,powerset(X80),X81),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(X79,powerset(X80),X81),X83)) = apply(sK5,sK13(X82,sK13(X79,powerset(X80),X81),X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_830])]) ).
fof(f4790,plain,
( ! [X82,X83,X80,X81,X79] :
( sP2(X79,powerset(X80),X81)
| element(sK13(X82,sK13(X79,powerset(X80),X81),X83),X80)
| in(sK13(X79,powerset(X80),X81),X81)
| sP2(X82,sK13(X79,powerset(X80),X81),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(X79,powerset(X80),X81),X83)) = apply(sK5,sK13(X82,sK13(X79,powerset(X80),X81),X83)) )
| ~ spl22_225
| ~ spl22_382 ),
inference(resolution,[],[f4571,f2223]) ).
fof(f15033,plain,
( spl22_829
| ~ spl22_229
| ~ spl22_382 ),
inference(avatar_split_clause,[],[f4789,f4570,f2271,f15031]) ).
fof(f15031,plain,
( spl22_829
<=> ! [X77,X74,X75,X78,X76] :
( sP2(X74,powerset(X75),X76)
| element(sK13(X77,X78,sK13(X74,powerset(X75),X76)),X75)
| in(sK13(X74,powerset(X75),X76),X76)
| sP2(X77,X78,sK13(X74,powerset(X75),X76))
| apply(sK5,sK13(X77,X78,sK13(X74,powerset(X75),X76))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(X74,powerset(X75),X76))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_829])]) ).
fof(f4789,plain,
( ! [X78,X76,X77,X74,X75] :
( sP2(X74,powerset(X75),X76)
| element(sK13(X77,X78,sK13(X74,powerset(X75),X76)),X75)
| in(sK13(X74,powerset(X75),X76),X76)
| sP2(X77,X78,sK13(X74,powerset(X75),X76))
| apply(sK5,sK13(X77,X78,sK13(X74,powerset(X75),X76))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(X74,powerset(X75),X76))) )
| ~ spl22_229
| ~ spl22_382 ),
inference(resolution,[],[f4571,f2272]) ).
fof(f15029,plain,
( spl22_828
| ~ spl22_226
| ~ spl22_382 ),
inference(avatar_split_clause,[],[f4788,f4570,f2237,f15027]) ).
fof(f15027,plain,
( spl22_828
<=> ! [X69,X73,X71,X70,X72] :
( sP2(X69,powerset(X70),X71)
| element(sK13(X72,X73,sK13(X69,powerset(X70),X71)),X70)
| in(sK13(X69,powerset(X70),X71),X71)
| sP2(X72,X73,sK13(X69,powerset(X70),X71))
| apply(sK5,sK13(X72,X73,sK13(X69,powerset(X70),X71))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(X69,powerset(X70),X71))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_828])]) ).
fof(f4788,plain,
( ! [X72,X70,X73,X71,X69] :
( sP2(X69,powerset(X70),X71)
| element(sK13(X72,X73,sK13(X69,powerset(X70),X71)),X70)
| in(sK13(X69,powerset(X70),X71),X71)
| sP2(X72,X73,sK13(X69,powerset(X70),X71))
| apply(sK5,sK13(X72,X73,sK13(X69,powerset(X70),X71))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(X69,powerset(X70),X71))) )
| ~ spl22_226
| ~ spl22_382 ),
inference(resolution,[],[f4571,f2238]) ).
fof(f15025,plain,
( spl22_827
| ~ spl22_228
| ~ spl22_380 ),
inference(avatar_split_clause,[],[f4735,f4562,f2256,f15023]) ).
fof(f15023,plain,
( spl22_827
<=> ! [X102,X101,X100,X99,X103] :
( sP2(X99,X100,powerset(X101))
| element(sK13(sK13(X99,X100,powerset(X101)),X102,X103),X101)
| in(sK13(X99,X100,powerset(X101)),X100)
| sP2(sK13(X99,X100,powerset(X101)),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(X99,X100,powerset(X101)),X102,X103)) = apply(sK5,sK13(sK13(X99,X100,powerset(X101)),X102,X103)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_827])]) ).
fof(f4562,plain,
( spl22_380
<=> ! [X5,X4,X7,X6] :
( in(sK13(X4,X5,powerset(X6)),X5)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_380])]) ).
fof(f4735,plain,
( ! [X101,X99,X102,X103,X100] :
( sP2(X99,X100,powerset(X101))
| element(sK13(sK13(X99,X100,powerset(X101)),X102,X103),X101)
| in(sK13(X99,X100,powerset(X101)),X100)
| sP2(sK13(X99,X100,powerset(X101)),X102,X103)
| apply(relation_dom_restriction(sK5,X103),sK13(sK13(X99,X100,powerset(X101)),X102,X103)) = apply(sK5,sK13(sK13(X99,X100,powerset(X101)),X102,X103)) )
| ~ spl22_228
| ~ spl22_380 ),
inference(resolution,[],[f4563,f2257]) ).
fof(f4563,plain,
( ! [X6,X7,X4,X5] :
( ~ in(X7,sK13(X4,X5,powerset(X6)))
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| in(sK13(X4,X5,powerset(X6)),X5) )
| ~ spl22_380 ),
inference(avatar_component_clause,[],[f4562]) ).
fof(f15021,plain,
( spl22_826
| ~ spl22_225
| ~ spl22_380 ),
inference(avatar_split_clause,[],[f4731,f4562,f2222,f15019]) ).
fof(f15019,plain,
( spl22_826
<=> ! [X79,X81,X82,X80,X83] :
( sP2(X79,X80,powerset(X81))
| element(sK13(X82,sK13(X79,X80,powerset(X81)),X83),X81)
| in(sK13(X79,X80,powerset(X81)),X80)
| sP2(X82,sK13(X79,X80,powerset(X81)),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(X79,X80,powerset(X81)),X83)) = apply(sK5,sK13(X82,sK13(X79,X80,powerset(X81)),X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_826])]) ).
fof(f4731,plain,
( ! [X82,X83,X80,X81,X79] :
( sP2(X79,X80,powerset(X81))
| element(sK13(X82,sK13(X79,X80,powerset(X81)),X83),X81)
| in(sK13(X79,X80,powerset(X81)),X80)
| sP2(X82,sK13(X79,X80,powerset(X81)),X83)
| apply(relation_dom_restriction(sK5,X83),sK13(X82,sK13(X79,X80,powerset(X81)),X83)) = apply(sK5,sK13(X82,sK13(X79,X80,powerset(X81)),X83)) )
| ~ spl22_225
| ~ spl22_380 ),
inference(resolution,[],[f4563,f2223]) ).
fof(f15017,plain,
( spl22_825
| ~ spl22_229
| ~ spl22_380 ),
inference(avatar_split_clause,[],[f4730,f4562,f2271,f15015]) ).
fof(f15015,plain,
( spl22_825
<=> ! [X77,X74,X75,X78,X76] :
( sP2(X74,X75,powerset(X76))
| element(sK13(X77,X78,sK13(X74,X75,powerset(X76))),X76)
| in(sK13(X74,X75,powerset(X76)),X75)
| sP2(X77,X78,sK13(X74,X75,powerset(X76)))
| apply(sK5,sK13(X77,X78,sK13(X74,X75,powerset(X76)))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(X74,X75,powerset(X76)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_825])]) ).
fof(f4730,plain,
( ! [X78,X76,X77,X74,X75] :
( sP2(X74,X75,powerset(X76))
| element(sK13(X77,X78,sK13(X74,X75,powerset(X76))),X76)
| in(sK13(X74,X75,powerset(X76)),X75)
| sP2(X77,X78,sK13(X74,X75,powerset(X76)))
| apply(sK5,sK13(X77,X78,sK13(X74,X75,powerset(X76)))) = apply(relation_dom_restriction(sK5,X77),sK13(X77,X78,sK13(X74,X75,powerset(X76)))) )
| ~ spl22_229
| ~ spl22_380 ),
inference(resolution,[],[f4563,f2272]) ).
fof(f15013,plain,
( spl22_824
| ~ spl22_226
| ~ spl22_380 ),
inference(avatar_split_clause,[],[f4729,f4562,f2237,f15011]) ).
fof(f15011,plain,
( spl22_824
<=> ! [X69,X73,X71,X70,X72] :
( sP2(X69,X70,powerset(X71))
| element(sK13(X72,X73,sK13(X69,X70,powerset(X71))),X71)
| in(sK13(X69,X70,powerset(X71)),X70)
| sP2(X72,X73,sK13(X69,X70,powerset(X71)))
| apply(sK5,sK13(X72,X73,sK13(X69,X70,powerset(X71)))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(X69,X70,powerset(X71)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_824])]) ).
fof(f4729,plain,
( ! [X72,X70,X73,X71,X69] :
( sP2(X69,X70,powerset(X71))
| element(sK13(X72,X73,sK13(X69,X70,powerset(X71))),X71)
| in(sK13(X69,X70,powerset(X71)),X70)
| sP2(X72,X73,sK13(X69,X70,powerset(X71)))
| apply(sK5,sK13(X72,X73,sK13(X69,X70,powerset(X71)))) = apply(relation_dom_restriction(sK5,X73),sK13(X72,X73,sK13(X69,X70,powerset(X71)))) )
| ~ spl22_226
| ~ spl22_380 ),
inference(resolution,[],[f4563,f2238]) ).
fof(f15009,plain,
( spl22_823
| ~ spl22_2
| ~ spl22_1
| ~ spl22_821 ),
inference(avatar_split_clause,[],[f14979,f14768,f219,f224,f15007]) ).
fof(f14768,plain,
( spl22_821
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_821])]) ).
fof(f14979,plain,
( ! [X11] :
( ~ function(sK5)
| relation_dom(relation_dom_restriction(sK5,X11)) = set_intersection2(relation_dom(sK5),X11) )
| ~ spl22_1
| ~ spl22_821 ),
inference(resolution,[],[f14769,f221]) ).
fof(f221,plain,
( relation(sK5)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f14769,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) )
| ~ spl22_821 ),
inference(avatar_component_clause,[],[f14768]) ).
fof(f14846,plain,
( spl22_822
| ~ spl22_56
| ~ spl22_790 ),
inference(avatar_split_clause,[],[f14177,f14026,f540,f14844]) ).
fof(f14026,plain,
( spl22_790
<=> ! [X17] :
( ~ sP0(sK5,sK6(X17))
| element(sK7(sK5,sK15),X17)
| empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_790])]) ).
fof(f14177,plain,
( ! [X5] :
( ~ sP0(sK5,sK6(X5))
| empty(X5)
| in(sK7(sK5,sK15),X5) )
| ~ spl22_56
| ~ spl22_790 ),
inference(duplicate_literal_removal,[],[f14176]) ).
fof(f14176,plain,
( ! [X5] :
( ~ sP0(sK5,sK6(X5))
| empty(X5)
| empty(X5)
| in(sK7(sK5,sK15),X5) )
| ~ spl22_56
| ~ spl22_790 ),
inference(resolution,[],[f14027,f541]) ).
fof(f14027,plain,
( ! [X17] :
( element(sK7(sK5,sK15),X17)
| ~ sP0(sK5,sK6(X17))
| empty(X17) )
| ~ spl22_790 ),
inference(avatar_component_clause,[],[f14026]) ).
fof(f14770,plain,
( spl22_821
| ~ spl22_58
| ~ spl22_345 ),
inference(avatar_split_clause,[],[f3825,f3763,f548,f14768]) ).
fof(f548,plain,
( spl22_58
<=> ! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_58])]) ).
fof(f3763,plain,
( spl22_345
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_345])]) ).
fof(f3825,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) )
| ~ spl22_58
| ~ spl22_345 ),
inference(duplicate_literal_removal,[],[f3822]) ).
fof(f3822,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_345 ),
inference(resolution,[],[f3764,f549]) ).
fof(f549,plain,
( ! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f3764,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) )
| ~ spl22_345 ),
inference(avatar_component_clause,[],[f3763]) ).
fof(f14766,plain,
( spl22_820
| ~ spl22_236
| ~ spl22_343 ),
inference(avatar_split_clause,[],[f3806,f3754,f2331,f14764]) ).
fof(f14764,plain,
( spl22_820
<=> ! [X6,X7] :
( subset(sK7(X6,powerset(X7)),X7)
| sP0(X6,powerset(X7))
| ~ sP0(X6,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_820])]) ).
fof(f3806,plain,
( ! [X6,X7] :
( subset(sK7(X6,powerset(X7)),X7)
| sP0(X6,powerset(X7))
| ~ sP0(X6,sK15) )
| ~ spl22_236
| ~ spl22_343 ),
inference(resolution,[],[f3755,f2332]) ).
fof(f14762,plain,
( spl22_819
| ~ spl22_197
| ~ spl22_304 ),
inference(avatar_split_clause,[],[f3254,f3237,f1926,f14760]) ).
fof(f14760,plain,
( spl22_819
<=> ! [X0] :
( ~ in(sK15,sK8(sK15,X0))
| sP0(sK15,X0)
| element(sK7(sK15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_819])]) ).
fof(f3237,plain,
( spl22_304
<=> ! [X8,X7] :
( element(sK7(X7,X8),X8)
| sP0(X7,X8)
| ~ in(relation_dom(X7),sK8(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_304])]) ).
fof(f3254,plain,
( ! [X0] :
( ~ in(sK15,sK8(sK15,X0))
| sP0(sK15,X0)
| element(sK7(sK15,X0),X0) )
| ~ spl22_197
| ~ spl22_304 ),
inference(superposition,[],[f3238,f1928]) ).
fof(f3238,plain,
( ! [X8,X7] :
( ~ in(relation_dom(X7),sK8(X7,X8))
| sP0(X7,X8)
| element(sK7(X7,X8),X8) )
| ~ spl22_304 ),
inference(avatar_component_clause,[],[f3237]) ).
fof(f14758,plain,
( spl22_818
| ~ spl22_197
| ~ spl22_302 ),
inference(avatar_split_clause,[],[f3248,f3229,f1926,f14756]) ).
fof(f14756,plain,
( spl22_818
<=> ! [X0] :
( element(sK8(sK15,X0),sK15)
| element(sK7(sK15,X0),X0)
| sP0(sK15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_818])]) ).
fof(f3248,plain,
( ! [X0] :
( element(sK8(sK15,X0),sK15)
| element(sK7(sK15,X0),X0)
| sP0(sK15,X0) )
| ~ spl22_197
| ~ spl22_302 ),
inference(superposition,[],[f3230,f1928]) ).
fof(f14754,plain,
( spl22_817
| ~ spl22_52
| ~ spl22_287 ),
inference(avatar_split_clause,[],[f3094,f3023,f498,f14752]) ).
fof(f14752,plain,
( spl22_817
<=> ! [X9,X8,X10] :
( ~ sP0(X8,powerset(X9))
| ~ in(X10,relation_dom(X8))
| subset(apply(X8,X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_817])]) ).
fof(f3094,plain,
( ! [X10,X8,X9] :
( ~ sP0(X8,powerset(X9))
| ~ in(X10,relation_dom(X8))
| subset(apply(X8,X10),X9) )
| ~ spl22_52
| ~ spl22_287 ),
inference(resolution,[],[f3024,f499]) ).
fof(f14750,plain,
( spl22_816
| ~ spl22_52
| ~ spl22_279 ),
inference(avatar_split_clause,[],[f2999,f2963,f498,f14748]) ).
fof(f14748,plain,
( spl22_816
<=> ! [X6,X7] :
( ~ empty(relation_dom(X6))
| sP0(X6,powerset(X7))
| subset(sK7(X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_816])]) ).
fof(f2999,plain,
( ! [X6,X7] :
( ~ empty(relation_dom(X6))
| sP0(X6,powerset(X7))
| subset(sK7(X6,powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_279 ),
inference(resolution,[],[f2964,f499]) ).
fof(f14746,plain,
( spl22_815
| ~ spl22_62
| ~ spl22_267 ),
inference(avatar_split_clause,[],[f2898,f2759,f598,f14744]) ).
fof(f14744,plain,
( spl22_815
<=> ! [X6,X7] :
( ~ empty(relation_dom(X6))
| ~ empty(X7)
| sK10(powerset(X7)) = relation_rng(X6)
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_815])]) ).
fof(f2759,plain,
( spl22_267
<=> ! [X13,X14] :
( sP0(X13,sK10(powerset(X14)))
| ~ empty(relation_dom(X13))
| ~ empty(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_267])]) ).
fof(f2898,plain,
( ! [X6,X7] :
( ~ empty(relation_dom(X6))
| ~ empty(X7)
| sK10(powerset(X7)) = relation_rng(X6)
| ~ sP1(X6) )
| ~ spl22_62
| ~ spl22_267 ),
inference(resolution,[],[f2760,f599]) ).
fof(f2760,plain,
( ! [X14,X13] :
( sP0(X13,sK10(powerset(X14)))
| ~ empty(relation_dom(X13))
| ~ empty(X14) )
| ~ spl22_267 ),
inference(avatar_component_clause,[],[f2759]) ).
fof(f14735,plain,
( spl22_814
| ~ spl22_52
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f2873,f2719,f498,f14733]) ).
fof(f14733,plain,
( spl22_814
<=> ! [X4] :
( empty(powerset(X4))
| empty(sK6(powerset(X4)))
| subset(sK10(sK6(powerset(X4))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_814])]) ).
fof(f2873,plain,
( ! [X4] :
( empty(powerset(X4))
| empty(sK6(powerset(X4)))
| subset(sK10(sK6(powerset(X4))),X4) )
| ~ spl22_52
| ~ spl22_257 ),
inference(resolution,[],[f2720,f499]) ).
fof(f14731,plain,
( spl22_813
| ~ spl22_74
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2677,f2571,f668,f14729]) ).
fof(f14729,plain,
( spl22_813
<=> ! [X29,X30,X31] :
( ~ sP0(X29,X30)
| ~ empty(X30)
| in(sK7(X29,X31),X31)
| sP0(X29,X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_813])]) ).
fof(f2677,plain,
( ! [X31,X29,X30] :
( ~ sP0(X29,X30)
| ~ empty(X30)
| in(sK7(X29,X31),X31)
| sP0(X29,X31) )
| ~ spl22_74
| ~ spl22_250 ),
inference(resolution,[],[f2572,f669]) ).
fof(f14727,plain,
( spl22_812
| ~ spl22_161
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2675,f2571,f1489,f14725]) ).
fof(f14725,plain,
( spl22_812
<=> ! [X25,X24,X23] :
( ~ sP0(X23,X24)
| ~ empty(X24)
| element(sK7(X23,X25),X25)
| sP0(X23,X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_812])]) ).
fof(f1489,plain,
( spl22_161
<=> ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_161])]) ).
fof(f2675,plain,
( ! [X24,X25,X23] :
( ~ sP0(X23,X24)
| ~ empty(X24)
| element(sK7(X23,X25),X25)
| sP0(X23,X25) )
| ~ spl22_161
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1490]) ).
fof(f1490,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| element(sK7(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl22_161 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f14723,plain,
( spl22_811
| ~ spl22_153
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2667,f2571,f1395,f14721]) ).
fof(f14721,plain,
( spl22_811
<=> ! [X0,X3,X2,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_811])]) ).
fof(f2667,plain,
( ! [X2,X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP0(X3,relation_dom(X0)) )
| ~ spl22_153
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1396]) ).
fof(f14719,plain,
( spl22_810
| ~ spl22_161
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1965,f1926,f1489,f14717]) ).
fof(f14717,plain,
( spl22_810
<=> ! [X8] :
( in(sK8(sK15,X8),sK15)
| element(sK7(sK15,X8),X8)
| sP0(sK15,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_810])]) ).
fof(f1965,plain,
( ! [X8] :
( in(sK8(sK15,X8),sK15)
| element(sK7(sK15,X8),X8)
| sP0(sK15,X8) )
| ~ spl22_161
| ~ spl22_197 ),
inference(superposition,[],[f1490,f1928]) ).
fof(f14715,plain,
( spl22_809
| ~ spl22_160
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1964,f1926,f1485,f14713]) ).
fof(f14713,plain,
( spl22_809
<=> ! [X7] :
( ~ in(sK15,sK8(sK15,X7))
| sP0(sK15,X7)
| in(sK7(sK15,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_809])]) ).
fof(f1485,plain,
( spl22_160
<=> ! [X2,X3] :
( in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ in(relation_dom(X2),sK8(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_160])]) ).
fof(f1964,plain,
( ! [X7] :
( ~ in(sK15,sK8(sK15,X7))
| sP0(sK15,X7)
| in(sK7(sK15,X7),X7) )
| ~ spl22_160
| ~ spl22_197 ),
inference(superposition,[],[f1486,f1928]) ).
fof(f1486,plain,
( ! [X2,X3] :
( ~ in(relation_dom(X2),sK8(X2,X3))
| sP0(X2,X3)
| in(sK7(X2,X3),X3) )
| ~ spl22_160 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f14711,plain,
( spl22_808
| ~ spl22_159
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1963,f1926,f1481,f14709]) ).
fof(f14709,plain,
( spl22_808
<=> ! [X6] :
( element(sK8(sK15,X6),sK15)
| in(sK7(sK15,X6),X6)
| sP0(sK15,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_808])]) ).
fof(f1963,plain,
( ! [X6] :
( element(sK8(sK15,X6),sK15)
| in(sK7(sK15,X6),X6)
| sP0(sK15,X6) )
| ~ spl22_159
| ~ spl22_197 ),
inference(superposition,[],[f1482,f1928]) ).
fof(f14707,plain,
( spl22_807
| ~ spl22_74
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1959,f1926,f668,f14705]) ).
fof(f14705,plain,
( spl22_807
<=> ! [X0] :
( in(sK8(sK15,X0),sK15)
| in(sK7(sK15,X0),X0)
| sP0(sK15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_807])]) ).
fof(f1959,plain,
( ! [X0] :
( in(sK8(sK15,X0),sK15)
| in(sK7(sK15,X0),X0)
| sP0(sK15,X0) )
| ~ spl22_74
| ~ spl22_197 ),
inference(superposition,[],[f669,f1928]) ).
fof(f14695,plain,
( spl22_591
| ~ spl22_806
| ~ spl22_775
| ~ spl22_791 ),
inference(avatar_split_clause,[],[f14549,f14127,f13734,f14692,f8049]) ).
fof(f8049,plain,
( spl22_591
<=> empty(apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_591])]) ).
fof(f14692,plain,
( spl22_806
<=> sP0(sK5,sK6(apply(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_806])]) ).
fof(f13734,plain,
( spl22_775
<=> ! [X5] :
( ~ sP0(sK5,sK6(X5))
| empty(X5)
| in(apply(sK5,sK4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_775])]) ).
fof(f14127,plain,
( spl22_791
<=> ! [X8] :
( empty(X8)
| ~ sP0(sK5,sK6(X8))
| ~ in(X8,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_791])]) ).
fof(f14549,plain,
( ~ sP0(sK5,sK6(apply(sK5,sK4)))
| empty(apply(sK5,sK4))
| ~ spl22_775
| ~ spl22_791 ),
inference(duplicate_literal_removal,[],[f14443]) ).
fof(f14443,plain,
( ~ sP0(sK5,sK6(apply(sK5,sK4)))
| empty(apply(sK5,sK4))
| empty(apply(sK5,sK4))
| ~ sP0(sK5,sK6(apply(sK5,sK4)))
| ~ spl22_775
| ~ spl22_791 ),
inference(resolution,[],[f14128,f13735]) ).
fof(f13735,plain,
( ! [X5] :
( in(apply(sK5,sK4),X5)
| empty(X5)
| ~ sP0(sK5,sK6(X5)) )
| ~ spl22_775 ),
inference(avatar_component_clause,[],[f13734]) ).
fof(f14128,plain,
( ! [X8] :
( ~ in(X8,apply(sK5,sK4))
| ~ sP0(sK5,sK6(X8))
| empty(X8) )
| ~ spl22_791 ),
inference(avatar_component_clause,[],[f14127]) ).
fof(f14682,plain,
( spl22_805
| ~ spl22_228
| ~ spl22_398 ),
inference(avatar_split_clause,[],[f5325,f5089,f2256,f14680]) ).
fof(f14680,plain,
( spl22_805
<=> ! [X88,X87,X89,X86] :
( sK7(X86,powerset(X87)) = apply(X86,sK8(X86,powerset(X87)))
| element(sK13(sK7(X86,powerset(X87)),X88,X89),X87)
| sP0(X86,powerset(X87))
| sP2(sK7(X86,powerset(X87)),X88,X89)
| apply(relation_dom_restriction(sK5,X89),sK13(sK7(X86,powerset(X87)),X88,X89)) = apply(sK5,sK13(sK7(X86,powerset(X87)),X88,X89)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_805])]) ).
fof(f5089,plain,
( spl22_398
<=> ! [X4,X5,X3] :
( sP0(X3,powerset(X4))
| sK7(X3,powerset(X4)) = apply(X3,sK8(X3,powerset(X4)))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_398])]) ).
fof(f5325,plain,
( ! [X88,X86,X89,X87] :
( sK7(X86,powerset(X87)) = apply(X86,sK8(X86,powerset(X87)))
| element(sK13(sK7(X86,powerset(X87)),X88,X89),X87)
| sP0(X86,powerset(X87))
| sP2(sK7(X86,powerset(X87)),X88,X89)
| apply(relation_dom_restriction(sK5,X89),sK13(sK7(X86,powerset(X87)),X88,X89)) = apply(sK5,sK13(sK7(X86,powerset(X87)),X88,X89)) )
| ~ spl22_228
| ~ spl22_398 ),
inference(resolution,[],[f5090,f2257]) ).
fof(f5090,plain,
( ! [X3,X4,X5] :
( ~ in(X5,sK7(X3,powerset(X4)))
| sK7(X3,powerset(X4)) = apply(X3,sK8(X3,powerset(X4)))
| element(X5,X4)
| sP0(X3,powerset(X4)) )
| ~ spl22_398 ),
inference(avatar_component_clause,[],[f5089]) ).
fof(f14678,plain,
( spl22_804
| ~ spl22_225
| ~ spl22_398 ),
inference(avatar_split_clause,[],[f5321,f5089,f2222,f14676]) ).
fof(f14676,plain,
( spl22_804
<=> ! [X73,X71,X70,X72] :
( sK7(X70,powerset(X71)) = apply(X70,sK8(X70,powerset(X71)))
| element(sK13(X72,sK7(X70,powerset(X71)),X73),X71)
| sP0(X70,powerset(X71))
| sP2(X72,sK7(X70,powerset(X71)),X73)
| apply(relation_dom_restriction(sK5,X73),sK13(X72,sK7(X70,powerset(X71)),X73)) = apply(sK5,sK13(X72,sK7(X70,powerset(X71)),X73)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_804])]) ).
fof(f5321,plain,
( ! [X72,X70,X73,X71] :
( sK7(X70,powerset(X71)) = apply(X70,sK8(X70,powerset(X71)))
| element(sK13(X72,sK7(X70,powerset(X71)),X73),X71)
| sP0(X70,powerset(X71))
| sP2(X72,sK7(X70,powerset(X71)),X73)
| apply(relation_dom_restriction(sK5,X73),sK13(X72,sK7(X70,powerset(X71)),X73)) = apply(sK5,sK13(X72,sK7(X70,powerset(X71)),X73)) )
| ~ spl22_225
| ~ spl22_398 ),
inference(resolution,[],[f5090,f2223]) ).
fof(f14674,plain,
( spl22_803
| ~ spl22_229
| ~ spl22_398 ),
inference(avatar_split_clause,[],[f5320,f5089,f2271,f14672]) ).
fof(f14672,plain,
( spl22_803
<=> ! [X68,X69,X67,X66] :
( sK7(X66,powerset(X67)) = apply(X66,sK8(X66,powerset(X67)))
| element(sK13(X68,X69,sK7(X66,powerset(X67))),X67)
| sP0(X66,powerset(X67))
| sP2(X68,X69,sK7(X66,powerset(X67)))
| apply(sK5,sK13(X68,X69,sK7(X66,powerset(X67)))) = apply(relation_dom_restriction(sK5,X68),sK13(X68,X69,sK7(X66,powerset(X67)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_803])]) ).
fof(f5320,plain,
( ! [X68,X69,X66,X67] :
( sK7(X66,powerset(X67)) = apply(X66,sK8(X66,powerset(X67)))
| element(sK13(X68,X69,sK7(X66,powerset(X67))),X67)
| sP0(X66,powerset(X67))
| sP2(X68,X69,sK7(X66,powerset(X67)))
| apply(sK5,sK13(X68,X69,sK7(X66,powerset(X67)))) = apply(relation_dom_restriction(sK5,X68),sK13(X68,X69,sK7(X66,powerset(X67)))) )
| ~ spl22_229
| ~ spl22_398 ),
inference(resolution,[],[f5090,f2272]) ).
fof(f14670,plain,
( spl22_802
| ~ spl22_226
| ~ spl22_398 ),
inference(avatar_split_clause,[],[f5319,f5089,f2237,f14668]) ).
fof(f14668,plain,
( spl22_802
<=> ! [X62,X64,X63,X65] :
( sK7(X62,powerset(X63)) = apply(X62,sK8(X62,powerset(X63)))
| element(sK13(X64,X65,sK7(X62,powerset(X63))),X63)
| sP0(X62,powerset(X63))
| sP2(X64,X65,sK7(X62,powerset(X63)))
| apply(sK5,sK13(X64,X65,sK7(X62,powerset(X63)))) = apply(relation_dom_restriction(sK5,X65),sK13(X64,X65,sK7(X62,powerset(X63)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_802])]) ).
fof(f5319,plain,
( ! [X65,X62,X63,X64] :
( sK7(X62,powerset(X63)) = apply(X62,sK8(X62,powerset(X63)))
| element(sK13(X64,X65,sK7(X62,powerset(X63))),X63)
| sP0(X62,powerset(X63))
| sP2(X64,X65,sK7(X62,powerset(X63)))
| apply(sK5,sK13(X64,X65,sK7(X62,powerset(X63)))) = apply(relation_dom_restriction(sK5,X65),sK13(X64,X65,sK7(X62,powerset(X63)))) )
| ~ spl22_226
| ~ spl22_398 ),
inference(resolution,[],[f5090,f2238]) ).
fof(f14615,plain,
( spl22_801
| ~ spl22_185
| ~ spl22_213 ),
inference(avatar_split_clause,[],[f2105,f2102,f1741,f14613]) ).
fof(f14613,plain,
( spl22_801
<=> ! [X2,X0,X1] :
( sP0(relation_dom_restriction(X0,X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK7(relation_dom_restriction(X0,X1),X2)) = apply(sK5,sK7(relation_dom_restriction(X0,X1),X2))
| apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2)) = apply(X0,sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_801])]) ).
fof(f2102,plain,
( spl22_213
<=> ! [X16,X17] :
( apply(relation_dom_restriction(sK5,X16),sK7(X17,X16)) = apply(sK5,sK7(X17,X16))
| sP0(X17,X16)
| in(sK8(X17,X16),relation_dom(X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_213])]) ).
fof(f2105,plain,
( ! [X2,X0,X1] :
( sP0(relation_dom_restriction(X0,X1),X2)
| apply(relation_dom_restriction(sK5,X2),sK7(relation_dom_restriction(X0,X1),X2)) = apply(sK5,sK7(relation_dom_restriction(X0,X1),X2))
| apply(relation_dom_restriction(X0,X1),sK8(relation_dom_restriction(X0,X1),X2)) = apply(X0,sK8(relation_dom_restriction(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_185
| ~ spl22_213 ),
inference(resolution,[],[f2103,f1742]) ).
fof(f2103,plain,
( ! [X16,X17] :
( in(sK8(X17,X16),relation_dom(X17))
| sP0(X17,X16)
| apply(relation_dom_restriction(sK5,X16),sK7(X17,X16)) = apply(sK5,sK7(X17,X16)) )
| ~ spl22_213 ),
inference(avatar_component_clause,[],[f2102]) ).
fof(f14193,plain,
( spl22_800
| ~ spl22_228
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5261,f5075,f2256,f14191]) ).
fof(f14191,plain,
( spl22_800
<=> ! [X166,X163,X164,X167,X165] :
( ~ sP0(X163,X164)
| apply(relation_dom_restriction(X165,X164),apply(X163,sK13(relation_dom(X163),X166,X167))) = apply(X165,apply(X163,sK13(relation_dom(X163),X166,X167)))
| ~ function(X165)
| ~ relation(X165)
| sP2(relation_dom(X163),X166,X167)
| apply(relation_dom_restriction(sK5,X167),sK13(relation_dom(X163),X166,X167)) = apply(sK5,sK13(relation_dom(X163),X166,X167)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_800])]) ).
fof(f5075,plain,
( spl22_396
<=> ! [X5,X4,X6,X3] :
( ~ in(X3,relation_dom(X4))
| ~ sP0(X4,X5)
| apply(relation_dom_restriction(X6,X5),apply(X4,X3)) = apply(X6,apply(X4,X3))
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_396])]) ).
fof(f5261,plain,
( ! [X163,X166,X167,X164,X165] :
( ~ sP0(X163,X164)
| apply(relation_dom_restriction(X165,X164),apply(X163,sK13(relation_dom(X163),X166,X167))) = apply(X165,apply(X163,sK13(relation_dom(X163),X166,X167)))
| ~ function(X165)
| ~ relation(X165)
| sP2(relation_dom(X163),X166,X167)
| apply(relation_dom_restriction(sK5,X167),sK13(relation_dom(X163),X166,X167)) = apply(sK5,sK13(relation_dom(X163),X166,X167)) )
| ~ spl22_228
| ~ spl22_396 ),
inference(resolution,[],[f5076,f2257]) ).
fof(f5076,plain,
( ! [X3,X6,X4,X5] :
( ~ in(X3,relation_dom(X4))
| ~ sP0(X4,X5)
| apply(relation_dom_restriction(X6,X5),apply(X4,X3)) = apply(X6,apply(X4,X3))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_396 ),
inference(avatar_component_clause,[],[f5075]) ).
fof(f14189,plain,
( spl22_799
| ~ spl22_225
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5257,f5075,f2222,f14187]) ).
fof(f14187,plain,
( spl22_799
<=> ! [X147,X143,X146,X145,X144] :
( ~ sP0(X143,X144)
| apply(relation_dom_restriction(X145,X144),apply(X143,sK13(X146,relation_dom(X143),X147))) = apply(X145,apply(X143,sK13(X146,relation_dom(X143),X147)))
| ~ function(X145)
| ~ relation(X145)
| sP2(X146,relation_dom(X143),X147)
| apply(relation_dom_restriction(sK5,X147),sK13(X146,relation_dom(X143),X147)) = apply(sK5,sK13(X146,relation_dom(X143),X147)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_799])]) ).
fof(f5257,plain,
( ! [X145,X143,X146,X147,X144] :
( ~ sP0(X143,X144)
| apply(relation_dom_restriction(X145,X144),apply(X143,sK13(X146,relation_dom(X143),X147))) = apply(X145,apply(X143,sK13(X146,relation_dom(X143),X147)))
| ~ function(X145)
| ~ relation(X145)
| sP2(X146,relation_dom(X143),X147)
| apply(relation_dom_restriction(sK5,X147),sK13(X146,relation_dom(X143),X147)) = apply(sK5,sK13(X146,relation_dom(X143),X147)) )
| ~ spl22_225
| ~ spl22_396 ),
inference(resolution,[],[f5076,f2223]) ).
fof(f14185,plain,
( spl22_798
| ~ spl22_229
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5256,f5075,f2271,f14183]) ).
fof(f14183,plain,
( spl22_798
<=> ! [X139,X140,X142,X141,X138] :
( ~ sP0(X138,X139)
| apply(relation_dom_restriction(X140,X139),apply(X138,sK13(X141,X142,relation_dom(X138)))) = apply(X140,apply(X138,sK13(X141,X142,relation_dom(X138))))
| ~ function(X140)
| ~ relation(X140)
| sP2(X141,X142,relation_dom(X138))
| apply(sK5,sK13(X141,X142,relation_dom(X138))) = apply(relation_dom_restriction(sK5,X141),sK13(X141,X142,relation_dom(X138))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_798])]) ).
fof(f5256,plain,
( ! [X142,X140,X141,X138,X139] :
( ~ sP0(X138,X139)
| apply(relation_dom_restriction(X140,X139),apply(X138,sK13(X141,X142,relation_dom(X138)))) = apply(X140,apply(X138,sK13(X141,X142,relation_dom(X138))))
| ~ function(X140)
| ~ relation(X140)
| sP2(X141,X142,relation_dom(X138))
| apply(sK5,sK13(X141,X142,relation_dom(X138))) = apply(relation_dom_restriction(sK5,X141),sK13(X141,X142,relation_dom(X138))) )
| ~ spl22_229
| ~ spl22_396 ),
inference(resolution,[],[f5076,f2272]) ).
fof(f14181,plain,
( spl22_797
| ~ spl22_226
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5255,f5075,f2237,f14179]) ).
fof(f14179,plain,
( spl22_797
<=> ! [X133,X137,X136,X135,X134] :
( ~ sP0(X133,X134)
| apply(relation_dom_restriction(X135,X134),apply(X133,sK13(X136,X137,relation_dom(X133)))) = apply(X135,apply(X133,sK13(X136,X137,relation_dom(X133))))
| ~ function(X135)
| ~ relation(X135)
| sP2(X136,X137,relation_dom(X133))
| apply(sK5,sK13(X136,X137,relation_dom(X133))) = apply(relation_dom_restriction(sK5,X137),sK13(X136,X137,relation_dom(X133))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_797])]) ).
fof(f5255,plain,
( ! [X133,X136,X134,X137,X135] :
( ~ sP0(X133,X134)
| apply(relation_dom_restriction(X135,X134),apply(X133,sK13(X136,X137,relation_dom(X133)))) = apply(X135,apply(X133,sK13(X136,X137,relation_dom(X133))))
| ~ function(X135)
| ~ relation(X135)
| sP2(X136,X137,relation_dom(X133))
| apply(sK5,sK13(X136,X137,relation_dom(X133))) = apply(relation_dom_restriction(sK5,X137),sK13(X136,X137,relation_dom(X133))) )
| ~ spl22_226
| ~ spl22_396 ),
inference(resolution,[],[f5076,f2238]) ).
fof(f14172,plain,
( spl22_796
| ~ spl22_212
| ~ spl22_387 ),
inference(avatar_split_clause,[],[f4883,f4590,f2089,f14170]) ).
fof(f14170,plain,
( spl22_796
<=> ! [X5,X7,X6,X8] :
( sP2(powerset(X5),X6,X7)
| element(sK7(X8,sK13(powerset(X5),X6,X7)),X5)
| in(sK13(powerset(X5),X6,X7),X7)
| sP0(X8,sK13(powerset(X5),X6,X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(powerset(X5),X6,X7))) = apply(sK5,sK8(X8,sK13(powerset(X5),X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_796])]) ).
fof(f4883,plain,
( ! [X8,X6,X7,X5] :
( sP2(powerset(X5),X6,X7)
| element(sK7(X8,sK13(powerset(X5),X6,X7)),X5)
| in(sK13(powerset(X5),X6,X7),X7)
| sP0(X8,sK13(powerset(X5),X6,X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(powerset(X5),X6,X7))) = apply(sK5,sK8(X8,sK13(powerset(X5),X6,X7))) )
| ~ spl22_212
| ~ spl22_387 ),
inference(resolution,[],[f4591,f2090]) ).
fof(f14168,plain,
( spl22_795
| ~ spl22_212
| ~ spl22_385 ),
inference(avatar_split_clause,[],[f4828,f4582,f2089,f14166]) ).
fof(f14166,plain,
( spl22_795
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,powerset(X7))
| element(sK7(X8,sK13(X5,X6,powerset(X7))),X7)
| in(sK13(X5,X6,powerset(X7)),X5)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_795])]) ).
fof(f4828,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,powerset(X7))
| element(sK7(X8,sK13(X5,X6,powerset(X7))),X7)
| in(sK13(X5,X6,powerset(X7)),X5)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) )
| ~ spl22_212
| ~ spl22_385 ),
inference(resolution,[],[f4583,f2090]) ).
fof(f14164,plain,
( spl22_794
| ~ spl22_212
| ~ spl22_382 ),
inference(avatar_split_clause,[],[f4773,f4570,f2089,f14162]) ).
fof(f14162,plain,
( spl22_794
<=> ! [X5,X7,X6,X8] :
( sP2(X5,powerset(X6),X7)
| element(sK7(X8,sK13(X5,powerset(X6),X7)),X6)
| in(sK13(X5,powerset(X6),X7),X7)
| sP0(X8,sK13(X5,powerset(X6),X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,powerset(X6),X7))) = apply(sK5,sK8(X8,sK13(X5,powerset(X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_794])]) ).
fof(f4773,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,powerset(X6),X7)
| element(sK7(X8,sK13(X5,powerset(X6),X7)),X6)
| in(sK13(X5,powerset(X6),X7),X7)
| sP0(X8,sK13(X5,powerset(X6),X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,powerset(X6),X7))) = apply(sK5,sK8(X8,sK13(X5,powerset(X6),X7))) )
| ~ spl22_212
| ~ spl22_382 ),
inference(resolution,[],[f4571,f2090]) ).
fof(f14160,plain,
( spl22_793
| ~ spl22_212
| ~ spl22_380 ),
inference(avatar_split_clause,[],[f4714,f4562,f2089,f14158]) ).
fof(f14158,plain,
( spl22_793
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,powerset(X7))
| element(sK7(X8,sK13(X5,X6,powerset(X7))),X7)
| in(sK13(X5,X6,powerset(X7)),X6)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_793])]) ).
fof(f4714,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,powerset(X7))
| element(sK7(X8,sK13(X5,X6,powerset(X7))),X7)
| in(sK13(X5,X6,powerset(X7)),X6)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) )
| ~ spl22_212
| ~ spl22_380 ),
inference(resolution,[],[f4563,f2090]) ).
fof(f14152,plain,
( spl22_792
| ~ spl22_212
| ~ spl22_398 ),
inference(avatar_split_clause,[],[f5305,f5089,f2089,f14150]) ).
fof(f14150,plain,
( spl22_792
<=> ! [X18,X16,X17] :
( sK7(X16,powerset(X17)) = apply(X16,sK8(X16,powerset(X17)))
| element(sK7(X18,sK7(X16,powerset(X17))),X17)
| sP0(X16,powerset(X17))
| sP0(X18,sK7(X16,powerset(X17)))
| apply(relation_dom_restriction(sK5,relation_dom(X18)),sK8(X18,sK7(X16,powerset(X17)))) = apply(sK5,sK8(X18,sK7(X16,powerset(X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_792])]) ).
fof(f5305,plain,
( ! [X18,X16,X17] :
( sK7(X16,powerset(X17)) = apply(X16,sK8(X16,powerset(X17)))
| element(sK7(X18,sK7(X16,powerset(X17))),X17)
| sP0(X16,powerset(X17))
| sP0(X18,sK7(X16,powerset(X17)))
| apply(relation_dom_restriction(sK5,relation_dom(X18)),sK8(X18,sK7(X16,powerset(X17)))) = apply(sK5,sK8(X18,sK7(X16,powerset(X17)))) )
| ~ spl22_212
| ~ spl22_398 ),
inference(resolution,[],[f5090,f2090]) ).
fof(f14129,plain,
( spl22_791
| ~ spl22_45
| ~ spl22_775 ),
inference(avatar_split_clause,[],[f13783,f13734,f448,f14127]) ).
fof(f13783,plain,
( ! [X8] :
( empty(X8)
| ~ sP0(sK5,sK6(X8))
| ~ in(X8,apply(sK5,sK4)) )
| ~ spl22_45
| ~ spl22_775 ),
inference(resolution,[],[f13735,f449]) ).
fof(f14028,plain,
( spl22_790
| ~ spl22_141
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4503,f3672,f1277,f14026]) ).
fof(f3672,plain,
( spl22_340
<=> ! [X0] :
( in(sK7(sK5,sK15),X0)
| ~ sP0(sK5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_340])]) ).
fof(f4503,plain,
( ! [X17] :
( ~ sP0(sK5,sK6(X17))
| element(sK7(sK5,sK15),X17)
| empty(X17) )
| ~ spl22_141
| ~ spl22_340 ),
inference(resolution,[],[f3673,f1278]) ).
fof(f3673,plain,
( ! [X0] :
( in(sK7(sK5,sK15),X0)
| ~ sP0(sK5,X0) )
| ~ spl22_340 ),
inference(avatar_component_clause,[],[f3672]) ).
fof(f13856,plain,
( spl22_789
| ~ spl22_236
| ~ spl22_315 ),
inference(avatar_split_clause,[],[f3534,f3327,f2331,f13854]) ).
fof(f13854,plain,
( spl22_789
<=> ! [X36,X37,X35] :
( ~ empty(X35)
| sP2(sK10(powerset(X35)),X36,relation_dom(X37))
| ~ sP0(X37,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_789])]) ).
fof(f3534,plain,
( ! [X36,X37,X35] :
( ~ empty(X35)
| sP2(sK10(powerset(X35)),X36,relation_dom(X37))
| ~ sP0(X37,sK15) )
| ~ spl22_236
| ~ spl22_315 ),
inference(resolution,[],[f3328,f2332]) ).
fof(f13852,plain,
( spl22_788
| ~ spl22_236
| ~ spl22_314 ),
inference(avatar_split_clause,[],[f3517,f3323,f2331,f13850]) ).
fof(f13850,plain,
( spl22_788
<=> ! [X36,X37,X35] :
( ~ empty(X35)
| sP2(X36,sK10(powerset(X35)),relation_dom(X37))
| ~ sP0(X37,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_788])]) ).
fof(f3517,plain,
( ! [X36,X37,X35] :
( ~ empty(X35)
| sP2(X36,sK10(powerset(X35)),relation_dom(X37))
| ~ sP0(X37,sK15) )
| ~ spl22_236
| ~ spl22_314 ),
inference(resolution,[],[f3324,f2332]) ).
fof(f13848,plain,
( spl22_787
| ~ spl22_131
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3504,f3319,f1173,f13846]) ).
fof(f13846,plain,
( spl22_787
<=> ! [X49,X48,X47] :
( ~ empty(X47)
| sP2(X48,sK10(powerset(X49)),sK10(powerset(X47)))
| ~ empty(X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_787])]) ).
fof(f3504,plain,
( ! [X48,X49,X47] :
( ~ empty(X47)
| sP2(X48,sK10(powerset(X49)),sK10(powerset(X47)))
| ~ empty(X49) )
| ~ spl22_131
| ~ spl22_313 ),
inference(resolution,[],[f3320,f1174]) ).
fof(f13844,plain,
( spl22_786
| ~ spl22_236
| ~ spl22_313 ),
inference(avatar_split_clause,[],[f3500,f3319,f2331,f13842]) ).
fof(f13842,plain,
( spl22_786
<=> ! [X34,X36,X35] :
( ~ empty(X34)
| sP2(X35,relation_dom(X36),sK10(powerset(X34)))
| ~ sP0(X36,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_786])]) ).
fof(f3500,plain,
( ! [X36,X34,X35] :
( ~ empty(X34)
| sP2(X35,relation_dom(X36),sK10(powerset(X34)))
| ~ sP0(X36,sK15) )
| ~ spl22_236
| ~ spl22_313 ),
inference(resolution,[],[f3320,f2332]) ).
fof(f13776,plain,
( spl22_785
| ~ spl22_131
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3470,f3315,f1173,f13774]) ).
fof(f13774,plain,
( spl22_785
<=> ! [X49,X48,X47] :
( ~ empty(X47)
| sP2(sK10(powerset(X48)),X49,sK10(powerset(X47)))
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_785])]) ).
fof(f3470,plain,
( ! [X48,X49,X47] :
( ~ empty(X47)
| sP2(sK10(powerset(X48)),X49,sK10(powerset(X47)))
| ~ empty(X48) )
| ~ spl22_131
| ~ spl22_312 ),
inference(resolution,[],[f3316,f1174]) ).
fof(f13772,plain,
( spl22_784
| ~ spl22_236
| ~ spl22_312 ),
inference(avatar_split_clause,[],[f3466,f3315,f2331,f13770]) ).
fof(f13770,plain,
( spl22_784
<=> ! [X34,X36,X35] :
( ~ empty(X34)
| sP2(relation_dom(X35),X36,sK10(powerset(X34)))
| ~ sP0(X35,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_784])]) ).
fof(f3466,plain,
( ! [X36,X34,X35] :
( ~ empty(X34)
| sP2(relation_dom(X35),X36,sK10(powerset(X34)))
| ~ sP0(X35,sK15) )
| ~ spl22_236
| ~ spl22_312 ),
inference(resolution,[],[f3316,f2332]) ).
fof(f13768,plain,
( spl22_783
| ~ spl22_250
| ~ spl22_306 ),
inference(avatar_split_clause,[],[f3276,f3256,f2571,f13766]) ).
fof(f3276,plain,
( ! [X3,X4,X5] :
( ~ empty(X3)
| sP0(X4,sK10(powerset(X3)))
| ~ sP0(X4,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_306 ),
inference(resolution,[],[f3257,f2572]) ).
fof(f13764,plain,
( spl22_782
| ~ spl22_45
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3089,f3019,f448,f13762]) ).
fof(f13762,plain,
( spl22_782
<=> ! [X16,X15] :
( ~ in(X15,relation_rng(X16))
| ~ sP1(X16)
| ~ in(relation_dom(X16),sK9(X16,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_782])]) ).
fof(f3089,plain,
( ! [X16,X15] :
( ~ in(X15,relation_rng(X16))
| ~ sP1(X16)
| ~ in(relation_dom(X16),sK9(X16,X15)) )
| ~ spl22_45
| ~ spl22_286 ),
inference(resolution,[],[f3020,f449]) ).
fof(f13760,plain,
( spl22_781
| ~ spl22_46
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3088,f3019,f452,f13758]) ).
fof(f13758,plain,
( spl22_781
<=> ! [X13,X14] :
( ~ in(X13,relation_rng(X14))
| ~ sP1(X14)
| element(sK9(X14,X13),relation_dom(X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_781])]) ).
fof(f3088,plain,
( ! [X14,X13] :
( ~ in(X13,relation_rng(X14))
| ~ sP1(X14)
| element(sK9(X14,X13),relation_dom(X14)) )
| ~ spl22_46
| ~ spl22_286 ),
inference(resolution,[],[f3020,f453]) ).
fof(f13756,plain,
( spl22_780
| ~ spl22_52
| ~ spl22_275 ),
inference(avatar_split_clause,[],[f2933,f2795,f498,f13754]) ).
fof(f13754,plain,
( spl22_780
<=> ! [X6,X7] :
( sP2(powerset(X6),X7,sK15)
| subset(sK13(powerset(X6),X7,sK15),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_780])]) ).
fof(f2933,plain,
( ! [X6,X7] :
( sP2(powerset(X6),X7,sK15)
| subset(sK13(powerset(X6),X7,sK15),X6) )
| ~ spl22_52
| ~ spl22_275 ),
inference(resolution,[],[f2796,f499]) ).
fof(f13752,plain,
( spl22_779
| ~ spl22_52
| ~ spl22_274 ),
inference(avatar_split_clause,[],[f2926,f2791,f498,f13750]) ).
fof(f13750,plain,
( spl22_779
<=> ! [X6,X7] :
( sP2(sK15,X6,powerset(X7))
| subset(sK13(sK15,X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_779])]) ).
fof(f2926,plain,
( ! [X6,X7] :
( sP2(sK15,X6,powerset(X7))
| subset(sK13(sK15,X6,powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_274 ),
inference(resolution,[],[f2792,f499]) ).
fof(f13748,plain,
( spl22_778
| ~ spl22_52
| ~ spl22_273 ),
inference(avatar_split_clause,[],[f2922,f2787,f498,f13746]) ).
fof(f13746,plain,
( spl22_778
<=> ! [X6,X7] :
( sP2(X6,powerset(X7),sK15)
| subset(sK13(X6,powerset(X7),sK15),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_778])]) ).
fof(f2922,plain,
( ! [X6,X7] :
( sP2(X6,powerset(X7),sK15)
| subset(sK13(X6,powerset(X7),sK15),X7) )
| ~ spl22_52
| ~ spl22_273 ),
inference(resolution,[],[f2788,f499]) ).
fof(f13744,plain,
( spl22_777
| ~ spl22_52
| ~ spl22_272 ),
inference(avatar_split_clause,[],[f2918,f2783,f498,f13742]) ).
fof(f13742,plain,
( spl22_777
<=> ! [X6,X7] :
( sP2(X6,sK15,powerset(X7))
| subset(sK13(X6,sK15,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_777])]) ).
fof(f2918,plain,
( ! [X6,X7] :
( sP2(X6,sK15,powerset(X7))
| subset(sK13(X6,sK15,powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_272 ),
inference(resolution,[],[f2784,f499]) ).
fof(f13740,plain,
( spl22_776
| ~ spl22_56
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2870,f2715,f540,f13738]) ).
fof(f13738,plain,
( spl22_776
<=> ! [X5] :
( empty(sK10(powerset(X5)))
| empty(X5)
| in(sK10(sK10(powerset(X5))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_776])]) ).
fof(f2870,plain,
( ! [X5] :
( empty(sK10(powerset(X5)))
| empty(X5)
| in(sK10(sK10(powerset(X5))),X5) )
| ~ spl22_56
| ~ spl22_256 ),
inference(resolution,[],[f2716,f541]) ).
fof(f13736,plain,
( spl22_775
| ~ spl22_56
| ~ spl22_660 ),
inference(avatar_split_clause,[],[f11226,f9971,f540,f13734]) ).
fof(f9971,plain,
( spl22_660
<=> ! [X20] :
( ~ sP0(sK5,sK6(X20))
| element(apply(sK5,sK4),X20)
| empty(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_660])]) ).
fof(f11226,plain,
( ! [X5] :
( ~ sP0(sK5,sK6(X5))
| empty(X5)
| in(apply(sK5,sK4),X5) )
| ~ spl22_56
| ~ spl22_660 ),
inference(duplicate_literal_removal,[],[f11225]) ).
fof(f11225,plain,
( ! [X5] :
( ~ sP0(sK5,sK6(X5))
| empty(X5)
| empty(X5)
| in(apply(sK5,sK4),X5) )
| ~ spl22_56
| ~ spl22_660 ),
inference(resolution,[],[f9972,f541]) ).
fof(f9972,plain,
( ! [X20] :
( element(apply(sK5,sK4),X20)
| ~ sP0(sK5,sK6(X20))
| empty(X20) )
| ~ spl22_660 ),
inference(avatar_component_clause,[],[f9971]) ).
fof(f13732,plain,
( spl22_774
| ~ spl22_52
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2869,f2715,f498,f13730]) ).
fof(f13730,plain,
( spl22_774
<=> ! [X4] :
( empty(sK10(powerset(powerset(X4))))
| subset(sK10(sK10(powerset(powerset(X4)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_774])]) ).
fof(f2869,plain,
( ! [X4] :
( empty(sK10(powerset(powerset(X4))))
| subset(sK10(sK10(powerset(powerset(X4)))),X4) )
| ~ spl22_52
| ~ spl22_256 ),
inference(resolution,[],[f2716,f499]) ).
fof(f13728,plain,
( spl22_773
| ~ spl22_156
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2693,f2571,f1407,f13726]) ).
fof(f13726,plain,
( spl22_773
<=> ! [X93,X91,X90,X92] :
( ~ sP0(X90,X91)
| ~ empty(X91)
| sP2(relation_dom(X90),X92,X93)
| ~ empty(X93) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_773])]) ).
fof(f2693,plain,
( ! [X90,X91,X92,X93] :
( ~ sP0(X90,X91)
| ~ empty(X91)
| sP2(relation_dom(X90),X92,X93)
| ~ empty(X93) )
| ~ spl22_156
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1408]) ).
fof(f13724,plain,
( spl22_772
| ~ spl22_154
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2689,f2571,f1399,f13722]) ).
fof(f13722,plain,
( spl22_772
<=> ! [X75,X74,X77,X76] :
( ~ sP0(X74,X75)
| ~ empty(X75)
| sP2(X76,relation_dom(X74),X77)
| ~ empty(X77) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_772])]) ).
fof(f2689,plain,
( ! [X76,X77,X74,X75] :
( ~ sP0(X74,X75)
| ~ empty(X75)
| sP2(X76,relation_dom(X74),X77)
| ~ empty(X77) )
| ~ spl22_154
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1400]) ).
fof(f13720,plain,
( spl22_771
| ~ spl22_157
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2682,f2571,f1411,f13718]) ).
fof(f13718,plain,
( spl22_771
<=> ! [X48,X47,X46,X49] :
( ~ sP0(X46,X47)
| ~ empty(X47)
| sP2(X48,X49,relation_dom(X46))
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_771])]) ).
fof(f2682,plain,
( ! [X48,X46,X49,X47] :
( ~ sP0(X46,X47)
| ~ empty(X47)
| sP2(X48,X49,relation_dom(X46))
| ~ empty(X48) )
| ~ spl22_157
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1412]) ).
fof(f13716,plain,
( spl22_770
| ~ spl22_155
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2681,f2571,f1403,f13714]) ).
fof(f13714,plain,
( spl22_770
<=> ! [X44,X43,X42,X45] :
( ~ sP0(X42,X43)
| ~ empty(X43)
| sP2(X44,X45,relation_dom(X42))
| ~ empty(X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_770])]) ).
fof(f2681,plain,
( ! [X44,X45,X42,X43] :
( ~ sP0(X42,X43)
| ~ empty(X43)
| sP2(X44,X45,relation_dom(X42))
| ~ empty(X45) )
| ~ spl22_155
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1404]) ).
fof(f13712,plain,
( spl22_769
| ~ spl22_149
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2671,f2571,f1362,f13710]) ).
fof(f13710,plain,
( spl22_769
<=> ! [X11,X12,X13] :
( ~ sP0(X11,X12)
| ~ empty(X12)
| sP0(X13,relation_dom(X11))
| ~ empty(relation_dom(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_769])]) ).
fof(f2671,plain,
( ! [X11,X12,X13] :
( ~ sP0(X11,X12)
| ~ empty(X12)
| sP0(X13,relation_dom(X11))
| ~ empty(relation_dom(X13)) )
| ~ spl22_149
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1363]) ).
fof(f13636,plain,
( spl22_768
| ~ spl22_228
| ~ spl22_360 ),
inference(avatar_split_clause,[],[f4102,f4039,f2256,f13634]) ).
fof(f13634,plain,
( spl22_768
<=> ! [X75,X77,X78,X76] :
( sP0(X75,powerset(X76))
| element(sK13(sK7(X75,powerset(X76)),X77,X78),X76)
| in(sK8(X75,powerset(X76)),relation_dom(X75))
| sP2(sK7(X75,powerset(X76)),X77,X78)
| apply(relation_dom_restriction(sK5,X78),sK13(sK7(X75,powerset(X76)),X77,X78)) = apply(sK5,sK13(sK7(X75,powerset(X76)),X77,X78)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_768])]) ).
fof(f4102,plain,
( ! [X78,X76,X77,X75] :
( sP0(X75,powerset(X76))
| element(sK13(sK7(X75,powerset(X76)),X77,X78),X76)
| in(sK8(X75,powerset(X76)),relation_dom(X75))
| sP2(sK7(X75,powerset(X76)),X77,X78)
| apply(relation_dom_restriction(sK5,X78),sK13(sK7(X75,powerset(X76)),X77,X78)) = apply(sK5,sK13(sK7(X75,powerset(X76)),X77,X78)) )
| ~ spl22_228
| ~ spl22_360 ),
inference(resolution,[],[f4040,f2257]) ).
fof(f13632,plain,
( spl22_767
| ~ spl22_225
| ~ spl22_360 ),
inference(avatar_split_clause,[],[f4098,f4039,f2222,f13630]) ).
fof(f13630,plain,
( spl22_767
<=> ! [X61,X60,X59,X62] :
( sP0(X59,powerset(X60))
| element(sK13(X61,sK7(X59,powerset(X60)),X62),X60)
| in(sK8(X59,powerset(X60)),relation_dom(X59))
| sP2(X61,sK7(X59,powerset(X60)),X62)
| apply(relation_dom_restriction(sK5,X62),sK13(X61,sK7(X59,powerset(X60)),X62)) = apply(sK5,sK13(X61,sK7(X59,powerset(X60)),X62)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_767])]) ).
fof(f4098,plain,
( ! [X59,X62,X60,X61] :
( sP0(X59,powerset(X60))
| element(sK13(X61,sK7(X59,powerset(X60)),X62),X60)
| in(sK8(X59,powerset(X60)),relation_dom(X59))
| sP2(X61,sK7(X59,powerset(X60)),X62)
| apply(relation_dom_restriction(sK5,X62),sK13(X61,sK7(X59,powerset(X60)),X62)) = apply(sK5,sK13(X61,sK7(X59,powerset(X60)),X62)) )
| ~ spl22_225
| ~ spl22_360 ),
inference(resolution,[],[f4040,f2223]) ).
fof(f13628,plain,
( spl22_766
| ~ spl22_229
| ~ spl22_360 ),
inference(avatar_split_clause,[],[f4097,f4039,f2271,f13626]) ).
fof(f13626,plain,
( spl22_766
<=> ! [X55,X57,X56,X58] :
( sP0(X55,powerset(X56))
| element(sK13(X57,X58,sK7(X55,powerset(X56))),X56)
| in(sK8(X55,powerset(X56)),relation_dom(X55))
| sP2(X57,X58,sK7(X55,powerset(X56)))
| apply(sK5,sK13(X57,X58,sK7(X55,powerset(X56)))) = apply(relation_dom_restriction(sK5,X57),sK13(X57,X58,sK7(X55,powerset(X56)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_766])]) ).
fof(f4097,plain,
( ! [X58,X56,X57,X55] :
( sP0(X55,powerset(X56))
| element(sK13(X57,X58,sK7(X55,powerset(X56))),X56)
| in(sK8(X55,powerset(X56)),relation_dom(X55))
| sP2(X57,X58,sK7(X55,powerset(X56)))
| apply(sK5,sK13(X57,X58,sK7(X55,powerset(X56)))) = apply(relation_dom_restriction(sK5,X57),sK13(X57,X58,sK7(X55,powerset(X56)))) )
| ~ spl22_229
| ~ spl22_360 ),
inference(resolution,[],[f4040,f2272]) ).
fof(f13624,plain,
( spl22_765
| ~ spl22_226
| ~ spl22_360 ),
inference(avatar_split_clause,[],[f4096,f4039,f2237,f13622]) ).
fof(f13622,plain,
( spl22_765
<=> ! [X51,X54,X53,X52] :
( sP0(X51,powerset(X52))
| element(sK13(X53,X54,sK7(X51,powerset(X52))),X52)
| in(sK8(X51,powerset(X52)),relation_dom(X51))
| sP2(X53,X54,sK7(X51,powerset(X52)))
| apply(sK5,sK13(X53,X54,sK7(X51,powerset(X52)))) = apply(relation_dom_restriction(sK5,X54),sK13(X53,X54,sK7(X51,powerset(X52)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_765])]) ).
fof(f4096,plain,
( ! [X51,X54,X52,X53] :
( sP0(X51,powerset(X52))
| element(sK13(X53,X54,sK7(X51,powerset(X52))),X52)
| in(sK8(X51,powerset(X52)),relation_dom(X51))
| sP2(X53,X54,sK7(X51,powerset(X52)))
| apply(sK5,sK13(X53,X54,sK7(X51,powerset(X52)))) = apply(relation_dom_restriction(sK5,X54),sK13(X53,X54,sK7(X51,powerset(X52)))) )
| ~ spl22_226
| ~ spl22_360 ),
inference(resolution,[],[f4040,f2238]) ).
fof(f13589,plain,
( spl22_764
| ~ spl22_212
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5228,f5075,f2089,f13587]) ).
fof(f13587,plain,
( spl22_764
<=> ! [X24,X23,X25,X26] :
( ~ sP0(X23,X24)
| apply(relation_dom_restriction(X25,X24),apply(X23,sK7(X26,relation_dom(X23)))) = apply(X25,apply(X23,sK7(X26,relation_dom(X23))))
| ~ function(X25)
| ~ relation(X25)
| sP0(X26,relation_dom(X23))
| apply(relation_dom_restriction(sK5,relation_dom(X26)),sK8(X26,relation_dom(X23))) = apply(sK5,sK8(X26,relation_dom(X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_764])]) ).
fof(f5228,plain,
( ! [X26,X24,X25,X23] :
( ~ sP0(X23,X24)
| apply(relation_dom_restriction(X25,X24),apply(X23,sK7(X26,relation_dom(X23)))) = apply(X25,apply(X23,sK7(X26,relation_dom(X23))))
| ~ function(X25)
| ~ relation(X25)
| sP0(X26,relation_dom(X23))
| apply(relation_dom_restriction(sK5,relation_dom(X26)),sK8(X26,relation_dom(X23))) = apply(sK5,sK8(X26,relation_dom(X23))) )
| ~ spl22_212
| ~ spl22_396 ),
inference(resolution,[],[f5076,f2090]) ).
fof(f13569,plain,
( spl22_763
| ~ spl22_513
| ~ spl22_740 ),
inference(avatar_split_clause,[],[f12505,f12172,f7070,f13567]) ).
fof(f13567,plain,
( spl22_763
<=> ! [X4,X5] :
( ~ sP1(X4)
| ~ sP0(X4,X5)
| ~ empty(X5)
| ~ sP0(sK5,relation_rng(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_763])]) ).
fof(f12172,plain,
( spl22_740
<=> ! [X4,X5,X3] :
( ~ in(X3,relation_rng(X4))
| ~ sP1(X4)
| ~ sP0(X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_740])]) ).
fof(f12505,plain,
( ! [X4,X5] :
( ~ sP1(X4)
| ~ sP0(X4,X5)
| ~ empty(X5)
| ~ sP0(sK5,relation_rng(X4)) )
| ~ spl22_513
| ~ spl22_740 ),
inference(resolution,[],[f12173,f7071]) ).
fof(f12173,plain,
( ! [X3,X4,X5] :
( ~ in(X3,relation_rng(X4))
| ~ sP1(X4)
| ~ sP0(X4,X5)
| ~ empty(X5) )
| ~ spl22_740 ),
inference(avatar_component_clause,[],[f12172]) ).
fof(f12680,plain,
( spl22_762
| ~ spl22_228
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5050,f4961,f2256,f12678]) ).
fof(f12678,plain,
( spl22_762
<=> ! [X77,X78,X80,X79] :
( sK7(X77,powerset(X78)) = apply(X77,sK8(X77,powerset(X78)))
| ~ empty(X78)
| sP0(X77,powerset(X78))
| sP2(sK7(X77,powerset(X78)),X79,X80)
| apply(relation_dom_restriction(sK5,X80),sK13(sK7(X77,powerset(X78)),X79,X80)) = apply(sK5,sK13(sK7(X77,powerset(X78)),X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_762])]) ).
fof(f5050,plain,
( ! [X80,X78,X79,X77] :
( sK7(X77,powerset(X78)) = apply(X77,sK8(X77,powerset(X78)))
| ~ empty(X78)
| sP0(X77,powerset(X78))
| sP2(sK7(X77,powerset(X78)),X79,X80)
| apply(relation_dom_restriction(sK5,X80),sK13(sK7(X77,powerset(X78)),X79,X80)) = apply(sK5,sK13(sK7(X77,powerset(X78)),X79,X80)) )
| ~ spl22_228
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2257]) ).
fof(f12676,plain,
( spl22_761
| ~ spl22_225
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5046,f4961,f2222,f12674]) ).
fof(f12674,plain,
( spl22_761
<=> ! [X61,X64,X63,X62] :
( sK7(X61,powerset(X62)) = apply(X61,sK8(X61,powerset(X62)))
| ~ empty(X62)
| sP0(X61,powerset(X62))
| sP2(X63,sK7(X61,powerset(X62)),X64)
| apply(relation_dom_restriction(sK5,X64),sK13(X63,sK7(X61,powerset(X62)),X64)) = apply(sK5,sK13(X63,sK7(X61,powerset(X62)),X64)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_761])]) ).
fof(f5046,plain,
( ! [X62,X63,X61,X64] :
( sK7(X61,powerset(X62)) = apply(X61,sK8(X61,powerset(X62)))
| ~ empty(X62)
| sP0(X61,powerset(X62))
| sP2(X63,sK7(X61,powerset(X62)),X64)
| apply(relation_dom_restriction(sK5,X64),sK13(X63,sK7(X61,powerset(X62)),X64)) = apply(sK5,sK13(X63,sK7(X61,powerset(X62)),X64)) )
| ~ spl22_225
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2223]) ).
fof(f12672,plain,
( spl22_760
| ~ spl22_229
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5045,f4961,f2271,f12670]) ).
fof(f12670,plain,
( spl22_760
<=> ! [X59,X57,X58,X60] :
( sK7(X57,powerset(X58)) = apply(X57,sK8(X57,powerset(X58)))
| ~ empty(X58)
| sP0(X57,powerset(X58))
| sP2(X59,X60,sK7(X57,powerset(X58)))
| apply(sK5,sK13(X59,X60,sK7(X57,powerset(X58)))) = apply(relation_dom_restriction(sK5,X59),sK13(X59,X60,sK7(X57,powerset(X58)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_760])]) ).
fof(f5045,plain,
( ! [X58,X59,X57,X60] :
( sK7(X57,powerset(X58)) = apply(X57,sK8(X57,powerset(X58)))
| ~ empty(X58)
| sP0(X57,powerset(X58))
| sP2(X59,X60,sK7(X57,powerset(X58)))
| apply(sK5,sK13(X59,X60,sK7(X57,powerset(X58)))) = apply(relation_dom_restriction(sK5,X59),sK13(X59,X60,sK7(X57,powerset(X58)))) )
| ~ spl22_229
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2272]) ).
fof(f12661,plain,
( spl22_759
| ~ spl22_226
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5044,f4961,f2237,f12659]) ).
fof(f12659,plain,
( spl22_759
<=> ! [X55,X54,X53,X56] :
( sK7(X53,powerset(X54)) = apply(X53,sK8(X53,powerset(X54)))
| ~ empty(X54)
| sP0(X53,powerset(X54))
| sP2(X55,X56,sK7(X53,powerset(X54)))
| apply(sK5,sK13(X55,X56,sK7(X53,powerset(X54)))) = apply(relation_dom_restriction(sK5,X56),sK13(X55,X56,sK7(X53,powerset(X54)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_759])]) ).
fof(f5044,plain,
( ! [X56,X54,X55,X53] :
( sK7(X53,powerset(X54)) = apply(X53,sK8(X53,powerset(X54)))
| ~ empty(X54)
| sP0(X53,powerset(X54))
| sP2(X55,X56,sK7(X53,powerset(X54)))
| apply(sK5,sK13(X55,X56,sK7(X53,powerset(X54)))) = apply(relation_dom_restriction(sK5,X56),sK13(X55,X56,sK7(X53,powerset(X54)))) )
| ~ spl22_226
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2238]) ).
fof(f12657,plain,
( spl22_758
| ~ spl22_228
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4472,f4164,f2256,f12655]) ).
fof(f12655,plain,
( spl22_758
<=> ! [X99,X98,X100,X97,X96] :
( sP2(powerset(X96),X97,X98)
| ~ empty(X96)
| in(sK13(powerset(X96),X97,X98),X98)
| sP2(sK13(powerset(X96),X97,X98),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(powerset(X96),X97,X98),X99,X100)) = apply(sK5,sK13(sK13(powerset(X96),X97,X98),X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_758])]) ).
fof(f4472,plain,
( ! [X98,X99,X96,X97,X100] :
( sP2(powerset(X96),X97,X98)
| ~ empty(X96)
| in(sK13(powerset(X96),X97,X98),X98)
| sP2(sK13(powerset(X96),X97,X98),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(powerset(X96),X97,X98),X99,X100)) = apply(sK5,sK13(sK13(powerset(X96),X97,X98),X99,X100)) )
| ~ spl22_228
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2257]) ).
fof(f12653,plain,
( spl22_757
| ~ spl22_225
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4468,f4164,f2222,f12651]) ).
fof(f12651,plain,
( spl22_757
<=> ! [X77,X76,X78,X80,X79] :
( sP2(powerset(X76),X77,X78)
| ~ empty(X76)
| in(sK13(powerset(X76),X77,X78),X78)
| sP2(X79,sK13(powerset(X76),X77,X78),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(powerset(X76),X77,X78),X80)) = apply(sK5,sK13(X79,sK13(powerset(X76),X77,X78),X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_757])]) ).
fof(f4468,plain,
( ! [X80,X78,X79,X76,X77] :
( sP2(powerset(X76),X77,X78)
| ~ empty(X76)
| in(sK13(powerset(X76),X77,X78),X78)
| sP2(X79,sK13(powerset(X76),X77,X78),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(powerset(X76),X77,X78),X80)) = apply(sK5,sK13(X79,sK13(powerset(X76),X77,X78),X80)) )
| ~ spl22_225
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2223]) ).
fof(f12649,plain,
( spl22_756
| ~ spl22_229
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4467,f4164,f2271,f12647]) ).
fof(f12647,plain,
( spl22_756
<=> ! [X74,X71,X75,X73,X72] :
( sP2(powerset(X71),X72,X73)
| ~ empty(X71)
| in(sK13(powerset(X71),X72,X73),X73)
| sP2(X74,X75,sK13(powerset(X71),X72,X73))
| apply(sK5,sK13(X74,X75,sK13(powerset(X71),X72,X73))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(powerset(X71),X72,X73))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_756])]) ).
fof(f4467,plain,
( ! [X72,X73,X71,X74,X75] :
( sP2(powerset(X71),X72,X73)
| ~ empty(X71)
| in(sK13(powerset(X71),X72,X73),X73)
| sP2(X74,X75,sK13(powerset(X71),X72,X73))
| apply(sK5,sK13(X74,X75,sK13(powerset(X71),X72,X73))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(powerset(X71),X72,X73))) )
| ~ spl22_229
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2272]) ).
fof(f12645,plain,
( spl22_755
| ~ spl22_226
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4466,f4164,f2237,f12643]) ).
fof(f12643,plain,
( spl22_755
<=> ! [X69,X68,X70,X67,X66] :
( sP2(powerset(X66),X67,X68)
| ~ empty(X66)
| in(sK13(powerset(X66),X67,X68),X68)
| sP2(X69,X70,sK13(powerset(X66),X67,X68))
| apply(sK5,sK13(X69,X70,sK13(powerset(X66),X67,X68))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(powerset(X66),X67,X68))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_755])]) ).
fof(f4466,plain,
( ! [X70,X68,X69,X66,X67] :
( sP2(powerset(X66),X67,X68)
| ~ empty(X66)
| in(sK13(powerset(X66),X67,X68),X68)
| sP2(X69,X70,sK13(powerset(X66),X67,X68))
| apply(sK5,sK13(X69,X70,sK13(powerset(X66),X67,X68))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(powerset(X66),X67,X68))) )
| ~ spl22_226
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2238]) ).
fof(f12641,plain,
( spl22_754
| ~ spl22_228
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4421,f4156,f2256,f12639]) ).
fof(f12639,plain,
( spl22_754
<=> ! [X99,X98,X100,X97,X96] :
( sP2(X96,X97,powerset(X98))
| ~ empty(X98)
| in(sK13(X96,X97,powerset(X98)),X96)
| sP2(sK13(X96,X97,powerset(X98)),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(X96,X97,powerset(X98)),X99,X100)) = apply(sK5,sK13(sK13(X96,X97,powerset(X98)),X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_754])]) ).
fof(f4421,plain,
( ! [X98,X99,X96,X97,X100] :
( sP2(X96,X97,powerset(X98))
| ~ empty(X98)
| in(sK13(X96,X97,powerset(X98)),X96)
| sP2(sK13(X96,X97,powerset(X98)),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(X96,X97,powerset(X98)),X99,X100)) = apply(sK5,sK13(sK13(X96,X97,powerset(X98)),X99,X100)) )
| ~ spl22_228
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2257]) ).
fof(f12637,plain,
( spl22_753
| ~ spl22_225
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4417,f4156,f2222,f12635]) ).
fof(f12635,plain,
( spl22_753
<=> ! [X77,X76,X78,X80,X79] :
( sP2(X76,X77,powerset(X78))
| ~ empty(X78)
| in(sK13(X76,X77,powerset(X78)),X76)
| sP2(X79,sK13(X76,X77,powerset(X78)),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(X76,X77,powerset(X78)),X80)) = apply(sK5,sK13(X79,sK13(X76,X77,powerset(X78)),X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_753])]) ).
fof(f4417,plain,
( ! [X80,X78,X79,X76,X77] :
( sP2(X76,X77,powerset(X78))
| ~ empty(X78)
| in(sK13(X76,X77,powerset(X78)),X76)
| sP2(X79,sK13(X76,X77,powerset(X78)),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(X76,X77,powerset(X78)),X80)) = apply(sK5,sK13(X79,sK13(X76,X77,powerset(X78)),X80)) )
| ~ spl22_225
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2223]) ).
fof(f12633,plain,
( spl22_752
| ~ spl22_229
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4416,f4156,f2271,f12631]) ).
fof(f12631,plain,
( spl22_752
<=> ! [X74,X71,X75,X73,X72] :
( sP2(X71,X72,powerset(X73))
| ~ empty(X73)
| in(sK13(X71,X72,powerset(X73)),X71)
| sP2(X74,X75,sK13(X71,X72,powerset(X73)))
| apply(sK5,sK13(X74,X75,sK13(X71,X72,powerset(X73)))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(X71,X72,powerset(X73)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_752])]) ).
fof(f4416,plain,
( ! [X72,X73,X71,X74,X75] :
( sP2(X71,X72,powerset(X73))
| ~ empty(X73)
| in(sK13(X71,X72,powerset(X73)),X71)
| sP2(X74,X75,sK13(X71,X72,powerset(X73)))
| apply(sK5,sK13(X74,X75,sK13(X71,X72,powerset(X73)))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(X71,X72,powerset(X73)))) )
| ~ spl22_229
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2272]) ).
fof(f12629,plain,
( spl22_751
| ~ spl22_226
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4415,f4156,f2237,f12627]) ).
fof(f12627,plain,
( spl22_751
<=> ! [X69,X68,X70,X67,X66] :
( sP2(X66,X67,powerset(X68))
| ~ empty(X68)
| in(sK13(X66,X67,powerset(X68)),X66)
| sP2(X69,X70,sK13(X66,X67,powerset(X68)))
| apply(sK5,sK13(X69,X70,sK13(X66,X67,powerset(X68)))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(X66,X67,powerset(X68)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_751])]) ).
fof(f4415,plain,
( ! [X70,X68,X69,X66,X67] :
( sP2(X66,X67,powerset(X68))
| ~ empty(X68)
| in(sK13(X66,X67,powerset(X68)),X66)
| sP2(X69,X70,sK13(X66,X67,powerset(X68)))
| apply(sK5,sK13(X69,X70,sK13(X66,X67,powerset(X68)))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(X66,X67,powerset(X68)))) )
| ~ spl22_226
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2238]) ).
fof(f12625,plain,
( spl22_750
| ~ spl22_228
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4370,f4148,f2256,f12623]) ).
fof(f12623,plain,
( spl22_750
<=> ! [X99,X98,X100,X97,X96] :
( sP2(X96,powerset(X97),X98)
| ~ empty(X97)
| in(sK13(X96,powerset(X97),X98),X98)
| sP2(sK13(X96,powerset(X97),X98),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(X96,powerset(X97),X98),X99,X100)) = apply(sK5,sK13(sK13(X96,powerset(X97),X98),X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_750])]) ).
fof(f4370,plain,
( ! [X98,X99,X96,X97,X100] :
( sP2(X96,powerset(X97),X98)
| ~ empty(X97)
| in(sK13(X96,powerset(X97),X98),X98)
| sP2(sK13(X96,powerset(X97),X98),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(X96,powerset(X97),X98),X99,X100)) = apply(sK5,sK13(sK13(X96,powerset(X97),X98),X99,X100)) )
| ~ spl22_228
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2257]) ).
fof(f12621,plain,
( spl22_749
| ~ spl22_225
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4366,f4148,f2222,f12619]) ).
fof(f12619,plain,
( spl22_749
<=> ! [X77,X76,X78,X80,X79] :
( sP2(X76,powerset(X77),X78)
| ~ empty(X77)
| in(sK13(X76,powerset(X77),X78),X78)
| sP2(X79,sK13(X76,powerset(X77),X78),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(X76,powerset(X77),X78),X80)) = apply(sK5,sK13(X79,sK13(X76,powerset(X77),X78),X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_749])]) ).
fof(f4366,plain,
( ! [X80,X78,X79,X76,X77] :
( sP2(X76,powerset(X77),X78)
| ~ empty(X77)
| in(sK13(X76,powerset(X77),X78),X78)
| sP2(X79,sK13(X76,powerset(X77),X78),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(X76,powerset(X77),X78),X80)) = apply(sK5,sK13(X79,sK13(X76,powerset(X77),X78),X80)) )
| ~ spl22_225
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2223]) ).
fof(f12617,plain,
( spl22_748
| ~ spl22_229
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4365,f4148,f2271,f12615]) ).
fof(f12615,plain,
( spl22_748
<=> ! [X74,X71,X75,X73,X72] :
( sP2(X71,powerset(X72),X73)
| ~ empty(X72)
| in(sK13(X71,powerset(X72),X73),X73)
| sP2(X74,X75,sK13(X71,powerset(X72),X73))
| apply(sK5,sK13(X74,X75,sK13(X71,powerset(X72),X73))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(X71,powerset(X72),X73))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_748])]) ).
fof(f4365,plain,
( ! [X72,X73,X71,X74,X75] :
( sP2(X71,powerset(X72),X73)
| ~ empty(X72)
| in(sK13(X71,powerset(X72),X73),X73)
| sP2(X74,X75,sK13(X71,powerset(X72),X73))
| apply(sK5,sK13(X74,X75,sK13(X71,powerset(X72),X73))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(X71,powerset(X72),X73))) )
| ~ spl22_229
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2272]) ).
fof(f12613,plain,
( spl22_747
| ~ spl22_226
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4364,f4148,f2237,f12611]) ).
fof(f12611,plain,
( spl22_747
<=> ! [X69,X68,X70,X67,X66] :
( sP2(X66,powerset(X67),X68)
| ~ empty(X67)
| in(sK13(X66,powerset(X67),X68),X68)
| sP2(X69,X70,sK13(X66,powerset(X67),X68))
| apply(sK5,sK13(X69,X70,sK13(X66,powerset(X67),X68))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(X66,powerset(X67),X68))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_747])]) ).
fof(f4364,plain,
( ! [X70,X68,X69,X66,X67] :
( sP2(X66,powerset(X67),X68)
| ~ empty(X67)
| in(sK13(X66,powerset(X67),X68),X68)
| sP2(X69,X70,sK13(X66,powerset(X67),X68))
| apply(sK5,sK13(X69,X70,sK13(X66,powerset(X67),X68))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(X66,powerset(X67),X68))) )
| ~ spl22_226
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2238]) ).
fof(f12609,plain,
( spl22_746
| ~ spl22_228
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4319,f4139,f2256,f12607]) ).
fof(f12607,plain,
( spl22_746
<=> ! [X99,X98,X100,X97,X96] :
( sP2(X96,X97,powerset(X98))
| ~ empty(X98)
| in(sK13(X96,X97,powerset(X98)),X97)
| sP2(sK13(X96,X97,powerset(X98)),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(X96,X97,powerset(X98)),X99,X100)) = apply(sK5,sK13(sK13(X96,X97,powerset(X98)),X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_746])]) ).
fof(f4319,plain,
( ! [X98,X99,X96,X97,X100] :
( sP2(X96,X97,powerset(X98))
| ~ empty(X98)
| in(sK13(X96,X97,powerset(X98)),X97)
| sP2(sK13(X96,X97,powerset(X98)),X99,X100)
| apply(relation_dom_restriction(sK5,X100),sK13(sK13(X96,X97,powerset(X98)),X99,X100)) = apply(sK5,sK13(sK13(X96,X97,powerset(X98)),X99,X100)) )
| ~ spl22_228
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2257]) ).
fof(f12605,plain,
( spl22_745
| ~ spl22_225
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4315,f4139,f2222,f12603]) ).
fof(f12603,plain,
( spl22_745
<=> ! [X77,X76,X78,X80,X79] :
( sP2(X76,X77,powerset(X78))
| ~ empty(X78)
| in(sK13(X76,X77,powerset(X78)),X77)
| sP2(X79,sK13(X76,X77,powerset(X78)),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(X76,X77,powerset(X78)),X80)) = apply(sK5,sK13(X79,sK13(X76,X77,powerset(X78)),X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_745])]) ).
fof(f4315,plain,
( ! [X80,X78,X79,X76,X77] :
( sP2(X76,X77,powerset(X78))
| ~ empty(X78)
| in(sK13(X76,X77,powerset(X78)),X77)
| sP2(X79,sK13(X76,X77,powerset(X78)),X80)
| apply(relation_dom_restriction(sK5,X80),sK13(X79,sK13(X76,X77,powerset(X78)),X80)) = apply(sK5,sK13(X79,sK13(X76,X77,powerset(X78)),X80)) )
| ~ spl22_225
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2223]) ).
fof(f12601,plain,
( spl22_744
| ~ spl22_229
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4314,f4139,f2271,f12599]) ).
fof(f12599,plain,
( spl22_744
<=> ! [X74,X71,X75,X73,X72] :
( sP2(X71,X72,powerset(X73))
| ~ empty(X73)
| in(sK13(X71,X72,powerset(X73)),X72)
| sP2(X74,X75,sK13(X71,X72,powerset(X73)))
| apply(sK5,sK13(X74,X75,sK13(X71,X72,powerset(X73)))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(X71,X72,powerset(X73)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_744])]) ).
fof(f4314,plain,
( ! [X72,X73,X71,X74,X75] :
( sP2(X71,X72,powerset(X73))
| ~ empty(X73)
| in(sK13(X71,X72,powerset(X73)),X72)
| sP2(X74,X75,sK13(X71,X72,powerset(X73)))
| apply(sK5,sK13(X74,X75,sK13(X71,X72,powerset(X73)))) = apply(relation_dom_restriction(sK5,X74),sK13(X74,X75,sK13(X71,X72,powerset(X73)))) )
| ~ spl22_229
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2272]) ).
fof(f12597,plain,
( spl22_743
| ~ spl22_226
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4313,f4139,f2237,f12595]) ).
fof(f12595,plain,
( spl22_743
<=> ! [X69,X68,X70,X67,X66] :
( sP2(X66,X67,powerset(X68))
| ~ empty(X68)
| in(sK13(X66,X67,powerset(X68)),X67)
| sP2(X69,X70,sK13(X66,X67,powerset(X68)))
| apply(sK5,sK13(X69,X70,sK13(X66,X67,powerset(X68)))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(X66,X67,powerset(X68)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_743])]) ).
fof(f4313,plain,
( ! [X70,X68,X69,X66,X67] :
( sP2(X66,X67,powerset(X68))
| ~ empty(X68)
| in(sK13(X66,X67,powerset(X68)),X67)
| sP2(X69,X70,sK13(X66,X67,powerset(X68)))
| apply(sK5,sK13(X69,X70,sK13(X66,X67,powerset(X68)))) = apply(relation_dom_restriction(sK5,X70),sK13(X69,X70,sK13(X66,X67,powerset(X68)))) )
| ~ spl22_226
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2238]) ).
fof(f12593,plain,
( spl22_742
| ~ spl22_212
| ~ spl22_360 ),
inference(avatar_split_clause,[],[f4082,f4039,f2089,f12591]) ).
fof(f12591,plain,
( spl22_742
<=> ! [X6,X4,X5] :
( sP0(X4,powerset(X5))
| element(sK7(X6,sK7(X4,powerset(X5))),X5)
| in(sK8(X4,powerset(X5)),relation_dom(X4))
| sP0(X6,sK7(X4,powerset(X5)))
| apply(relation_dom_restriction(sK5,relation_dom(X6)),sK8(X6,sK7(X4,powerset(X5)))) = apply(sK5,sK8(X6,sK7(X4,powerset(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_742])]) ).
fof(f4082,plain,
( ! [X6,X4,X5] :
( sP0(X4,powerset(X5))
| element(sK7(X6,sK7(X4,powerset(X5))),X5)
| in(sK8(X4,powerset(X5)),relation_dom(X4))
| sP0(X6,sK7(X4,powerset(X5)))
| apply(relation_dom_restriction(sK5,relation_dom(X6)),sK8(X6,sK7(X4,powerset(X5)))) = apply(sK5,sK8(X6,sK7(X4,powerset(X5)))) )
| ~ spl22_212
| ~ spl22_360 ),
inference(resolution,[],[f4040,f2090]) ).
fof(f12281,plain,
( spl22_741
| ~ spl22_28
| ~ spl22_591 ),
inference(avatar_split_clause,[],[f12005,f8049,f351,f12278]) ).
fof(f12278,plain,
( spl22_741
<=> function(apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_741])]) ).
fof(f12005,plain,
( function(apply(sK5,sK4))
| ~ spl22_28
| ~ spl22_591 ),
inference(resolution,[],[f8051,f352]) ).
fof(f8051,plain,
( empty(apply(sK5,sK4))
| ~ spl22_591 ),
inference(avatar_component_clause,[],[f8049]) ).
fof(f12174,plain,
( spl22_740
| ~ spl22_250
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3084,f3019,f2571,f12172]) ).
fof(f3084,plain,
( ! [X3,X4,X5] :
( ~ in(X3,relation_rng(X4))
| ~ sP1(X4)
| ~ sP0(X4,X5)
| ~ empty(X5) )
| ~ spl22_250
| ~ spl22_286 ),
inference(resolution,[],[f3020,f2572]) ).
fof(f12170,plain,
( spl22_739
| ~ spl22_45
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f2987,f2959,f448,f12168]) ).
fof(f12168,plain,
( spl22_739
<=> ! [X18,X16,X17] :
( ~ in(X16,X17)
| ~ in(X16,X18)
| ~ in(set_intersection2(X17,X18),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_739])]) ).
fof(f2987,plain,
( ! [X18,X16,X17] :
( ~ in(X16,X17)
| ~ in(X16,X18)
| ~ in(set_intersection2(X17,X18),X16) )
| ~ spl22_45
| ~ spl22_278 ),
inference(resolution,[],[f2960,f449]) ).
fof(f12166,plain,
( spl22_738
| ~ spl22_46
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f2986,f2959,f452,f12164]) ).
fof(f12164,plain,
( spl22_738
<=> ! [X13,X14,X15] :
( ~ in(X13,X14)
| ~ in(X13,X15)
| element(X13,set_intersection2(X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_738])]) ).
fof(f2986,plain,
( ! [X14,X15,X13] :
( ~ in(X13,X14)
| ~ in(X13,X15)
| element(X13,set_intersection2(X14,X15)) )
| ~ spl22_46
| ~ spl22_278 ),
inference(resolution,[],[f2960,f453]) ).
fof(f12162,plain,
( spl22_737
| ~ spl22_64
| ~ spl22_271 ),
inference(avatar_split_clause,[],[f2915,f2779,f606,f12160]) ).
fof(f12160,plain,
( spl22_737
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| ~ empty(X12)
| sK10(powerset(X12)) = set_intersection2(X13,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_737])]) ).
fof(f606,plain,
( spl22_64
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_64])]) ).
fof(f2779,plain,
( spl22_271
<=> ! [X22,X24,X23] :
( sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X22)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_271])]) ).
fof(f2915,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| ~ empty(X12)
| sK10(powerset(X12)) = set_intersection2(X13,X11) )
| ~ spl22_64
| ~ spl22_271 ),
inference(resolution,[],[f2780,f607]) ).
fof(f607,plain,
( ! [X2,X0,X1] :
( ~ sP2(X1,X0,X2)
| set_intersection2(X0,X1) = X2 )
| ~ spl22_64 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f2780,plain,
( ! [X24,X22,X23] :
( sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X22)
| ~ empty(X24) )
| ~ spl22_271 ),
inference(avatar_component_clause,[],[f2779]) ).
fof(f12004,plain,
( spl22_736
| ~ spl22_64
| ~ spl22_270 ),
inference(avatar_split_clause,[],[f2911,f2775,f606,f12002]) ).
fof(f12002,plain,
( spl22_736
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(X13,sK10(powerset(X12))) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_736])]) ).
fof(f2775,plain,
( spl22_270
<=> ! [X22,X21,X23] :
( sP2(sK10(powerset(X21)),X22,X23)
| ~ empty(X23)
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_270])]) ).
fof(f2911,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(X13,sK10(powerset(X12))) = X11 )
| ~ spl22_64
| ~ spl22_270 ),
inference(resolution,[],[f2776,f607]) ).
fof(f2776,plain,
( ! [X21,X22,X23] :
( sP2(sK10(powerset(X21)),X22,X23)
| ~ empty(X23)
| ~ empty(X21) )
| ~ spl22_270 ),
inference(avatar_component_clause,[],[f2775]) ).
fof(f12000,plain,
( spl22_735
| ~ spl22_64
| ~ spl22_269 ),
inference(avatar_split_clause,[],[f2907,f2771,f606,f11998]) ).
fof(f11998,plain,
( spl22_735
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| ~ empty(X12)
| sK10(powerset(X12)) = set_intersection2(X11,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_735])]) ).
fof(f2771,plain,
( spl22_269
<=> ! [X22,X24,X23] :
( sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X23)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_269])]) ).
fof(f2907,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| ~ empty(X12)
| sK10(powerset(X12)) = set_intersection2(X11,X13) )
| ~ spl22_64
| ~ spl22_269 ),
inference(resolution,[],[f2772,f607]) ).
fof(f2772,plain,
( ! [X24,X22,X23] :
( sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X23)
| ~ empty(X24) )
| ~ spl22_269 ),
inference(avatar_component_clause,[],[f2771]) ).
fof(f11996,plain,
( spl22_734
| ~ spl22_64
| ~ spl22_268 ),
inference(avatar_split_clause,[],[f2903,f2763,f606,f11994]) ).
fof(f11994,plain,
( spl22_734
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(sK10(powerset(X12)),X13) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_734])]) ).
fof(f2763,plain,
( spl22_268
<=> ! [X22,X21,X23] :
( sP2(X21,sK10(powerset(X22)),X23)
| ~ empty(X23)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_268])]) ).
fof(f2903,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(sK10(powerset(X12)),X13) = X11 )
| ~ spl22_64
| ~ spl22_268 ),
inference(resolution,[],[f2764,f607]) ).
fof(f2764,plain,
( ! [X21,X22,X23] :
( sP2(X21,sK10(powerset(X22)),X23)
| ~ empty(X23)
| ~ empty(X22) )
| ~ spl22_268 ),
inference(avatar_component_clause,[],[f2763]) ).
fof(f11992,plain,
( spl22_733
| ~ spl22_64
| ~ spl22_266 ),
inference(avatar_split_clause,[],[f2895,f2755,f606,f11990]) ).
fof(f11990,plain,
( spl22_733
<=> ! [X9,X8] :
( ~ empty(X8)
| sK10(powerset(X8)) = set_intersection2(X9,sK10(powerset(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_733])]) ).
fof(f2755,plain,
( spl22_266
<=> ! [X16,X15] :
( sP2(sK10(powerset(X15)),X16,sK10(powerset(X15)))
| ~ empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_266])]) ).
fof(f2895,plain,
( ! [X8,X9] :
( ~ empty(X8)
| sK10(powerset(X8)) = set_intersection2(X9,sK10(powerset(X8))) )
| ~ spl22_64
| ~ spl22_266 ),
inference(resolution,[],[f2756,f607]) ).
fof(f2756,plain,
( ! [X16,X15] :
( sP2(sK10(powerset(X15)),X16,sK10(powerset(X15)))
| ~ empty(X15) )
| ~ spl22_266 ),
inference(avatar_component_clause,[],[f2755]) ).
fof(f11988,plain,
( spl22_732
| ~ spl22_64
| ~ spl22_263 ),
inference(avatar_split_clause,[],[f2885,f2743,f606,f11986]) ).
fof(f11986,plain,
( spl22_732
<=> ! [X9,X8] :
( ~ empty(X8)
| sK10(powerset(X8)) = set_intersection2(sK10(powerset(X8)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_732])]) ).
fof(f2743,plain,
( spl22_263
<=> ! [X16,X15] :
( sP2(X15,sK10(powerset(X16)),sK10(powerset(X16)))
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_263])]) ).
fof(f2885,plain,
( ! [X8,X9] :
( ~ empty(X8)
| sK10(powerset(X8)) = set_intersection2(sK10(powerset(X8)),X9) )
| ~ spl22_64
| ~ spl22_263 ),
inference(resolution,[],[f2744,f607]) ).
fof(f2744,plain,
( ! [X16,X15] :
( sP2(X15,sK10(powerset(X16)),sK10(powerset(X16)))
| ~ empty(X16) )
| ~ spl22_263 ),
inference(avatar_component_clause,[],[f2743]) ).
fof(f11984,plain,
( spl22_731
| ~ spl22_146
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2696,f2571,f1316,f11982]) ).
fof(f11982,plain,
( spl22_731
<=> ! [X102,X101,X103] :
( ~ sP0(X101,X102)
| ~ empty(X102)
| sP2(relation_dom(X101),X103,relation_dom(X101)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_731])]) ).
fof(f2696,plain,
( ! [X101,X102,X103] :
( ~ sP0(X101,X102)
| ~ empty(X102)
| sP2(relation_dom(X101),X103,relation_dom(X101)) )
| ~ spl22_146
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1317]) ).
fof(f11980,plain,
( spl22_730
| ~ spl22_145
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2695,f2571,f1312,f11978]) ).
fof(f11978,plain,
( spl22_730
<=> ! [X98,X100,X99] :
( ~ sP0(X98,X99)
| ~ empty(X99)
| sP2(X100,relation_dom(X98),relation_dom(X98)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_730])]) ).
fof(f2695,plain,
( ! [X98,X99,X100] :
( ~ sP0(X98,X99)
| ~ empty(X99)
| sP2(X100,relation_dom(X98),relation_dom(X98)) )
| ~ spl22_145
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1313]) ).
fof(f11976,plain,
( spl22_729
| ~ spl22_216
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f2648,f2567,f2120,f11974]) ).
fof(f11974,plain,
( spl22_729
<=> ! [X6,X5] :
( relation_dom(relation_dom(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_729])]) ).
fof(f2120,plain,
( spl22_216
<=> ! [X4] :
( ~ empty(X4)
| empty(sK10(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_216])]) ).
fof(f2567,plain,
( spl22_249
<=> ! [X2,X3] :
( ~ empty(X2)
| relation_dom(relation_dom(X3)) = X2
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_249])]) ).
fof(f2648,plain,
( ! [X6,X5] :
( relation_dom(relation_dom(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) )
| ~ spl22_216
| ~ spl22_249 ),
inference(resolution,[],[f2568,f2121]) ).
fof(f2121,plain,
( ! [X4] :
( empty(sK10(powerset(X4)))
| ~ empty(X4) )
| ~ spl22_216 ),
inference(avatar_component_clause,[],[f2120]) ).
fof(f2568,plain,
( ! [X2,X3] :
( ~ empty(X3)
| relation_dom(relation_dom(X3)) = X2
| ~ empty(X2) )
| ~ spl22_249 ),
inference(avatar_component_clause,[],[f2567]) ).
fof(f11972,plain,
( spl22_728
| ~ spl22_216
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2626,f2563,f2120,f11970]) ).
fof(f11970,plain,
( spl22_728
<=> ! [X6,X5] :
( relation_dom(relation_rng(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_728])]) ).
fof(f2563,plain,
( spl22_248
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_248])]) ).
fof(f2626,plain,
( ! [X6,X5] :
( relation_dom(relation_rng(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) )
| ~ spl22_216
| ~ spl22_248 ),
inference(resolution,[],[f2564,f2121]) ).
fof(f2564,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl22_248 ),
inference(avatar_component_clause,[],[f2563]) ).
fof(f11968,plain,
( spl22_727
| ~ spl22_216
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f2604,f2559,f2120,f11966]) ).
fof(f11966,plain,
( spl22_727
<=> ! [X6,X5] :
( relation_rng(relation_dom(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_727])]) ).
fof(f2559,plain,
( spl22_247
<=> ! [X2,X3] :
( ~ empty(X2)
| relation_rng(relation_dom(X3)) = X2
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_247])]) ).
fof(f2604,plain,
( ! [X6,X5] :
( relation_rng(relation_dom(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) )
| ~ spl22_216
| ~ spl22_247 ),
inference(resolution,[],[f2560,f2121]) ).
fof(f2560,plain,
( ! [X2,X3] :
( ~ empty(X3)
| relation_rng(relation_dom(X3)) = X2
| ~ empty(X2) )
| ~ spl22_247 ),
inference(avatar_component_clause,[],[f2559]) ).
fof(f11964,plain,
( spl22_591
| ~ spl22_124
| ~ spl22_715 ),
inference(avatar_split_clause,[],[f11584,f11460,f1103,f8049]) ).
fof(f11460,plain,
( spl22_715
<=> ! [X1] : ~ in(X1,apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_715])]) ).
fof(f11584,plain,
( empty(apply(sK5,sK4))
| ~ spl22_124
| ~ spl22_715 ),
inference(resolution,[],[f11461,f1104]) ).
fof(f11461,plain,
( ! [X1] : ~ in(X1,apply(sK5,sK4))
| ~ spl22_715 ),
inference(avatar_component_clause,[],[f11460]) ).
fof(f11963,plain,
( spl22_726
| ~ spl22_216
| ~ spl22_246 ),
inference(avatar_split_clause,[],[f2577,f2555,f2120,f11961]) ).
fof(f11961,plain,
( spl22_726
<=> ! [X6,X5] :
( relation_rng(relation_rng(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_726])]) ).
fof(f2555,plain,
( spl22_246
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_246])]) ).
fof(f2577,plain,
( ! [X6,X5] :
( relation_rng(relation_rng(sK10(powerset(X5)))) = X6
| ~ empty(X6)
| ~ empty(X5) )
| ~ spl22_216
| ~ spl22_246 ),
inference(resolution,[],[f2556,f2121]) ).
fof(f2556,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl22_246 ),
inference(avatar_component_clause,[],[f2555]) ).
fof(f11959,plain,
( spl22_725
| ~ spl22_74
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2413,f2331,f668,f11957]) ).
fof(f11957,plain,
( spl22_725
<=> ! [X20,X19] :
( ~ sP0(X19,sK15)
| in(sK7(X19,X20),X20)
| sP0(X19,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_725])]) ).
fof(f2413,plain,
( ! [X19,X20] :
( ~ sP0(X19,sK15)
| in(sK7(X19,X20),X20)
| sP0(X19,X20) )
| ~ spl22_74
| ~ spl22_236 ),
inference(resolution,[],[f2332,f669]) ).
fof(f11955,plain,
( spl22_724
| ~ spl22_161
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2411,f2331,f1489,f11953]) ).
fof(f11953,plain,
( spl22_724
<=> ! [X16,X15] :
( ~ sP0(X15,sK15)
| element(sK7(X15,X16),X16)
| sP0(X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_724])]) ).
fof(f2411,plain,
( ! [X16,X15] :
( ~ sP0(X15,sK15)
| element(sK7(X15,X16),X16)
| sP0(X15,X16) )
| ~ spl22_161
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1490]) ).
fof(f11951,plain,
( spl22_723
| ~ spl22_153
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2403,f2331,f1395,f11949]) ).
fof(f11949,plain,
( spl22_723
<=> ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_723])]) ).
fof(f2403,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,sK15)
| ~ in(X1,relation_dom(X2))
| ~ sP0(X2,relation_dom(X0)) )
| ~ spl22_153
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1396]) ).
fof(f11653,plain,
( spl22_722
| ~ spl22_212
| ~ spl22_395 ),
inference(avatar_split_clause,[],[f5029,f4961,f2089,f11651]) ).
fof(f11651,plain,
( spl22_722
<=> ! [X6,X4,X5] :
( sK7(X4,powerset(X5)) = apply(X4,sK8(X4,powerset(X5)))
| ~ empty(X5)
| sP0(X4,powerset(X5))
| sP0(X6,sK7(X4,powerset(X5)))
| apply(relation_dom_restriction(sK5,relation_dom(X6)),sK8(X6,sK7(X4,powerset(X5)))) = apply(sK5,sK8(X6,sK7(X4,powerset(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_722])]) ).
fof(f5029,plain,
( ! [X6,X4,X5] :
( sK7(X4,powerset(X5)) = apply(X4,sK8(X4,powerset(X5)))
| ~ empty(X5)
| sP0(X4,powerset(X5))
| sP0(X6,sK7(X4,powerset(X5)))
| apply(relation_dom_restriction(sK5,relation_dom(X6)),sK8(X6,sK7(X4,powerset(X5)))) = apply(sK5,sK8(X6,sK7(X4,powerset(X5)))) )
| ~ spl22_212
| ~ spl22_395 ),
inference(resolution,[],[f4962,f2090]) ).
fof(f11569,plain,
( spl22_721
| ~ spl22_212
| ~ spl22_373 ),
inference(avatar_split_clause,[],[f4452,f4164,f2089,f11567]) ).
fof(f11567,plain,
( spl22_721
<=> ! [X5,X7,X6,X8] :
( sP2(powerset(X5),X6,X7)
| ~ empty(X5)
| in(sK13(powerset(X5),X6,X7),X7)
| sP0(X8,sK13(powerset(X5),X6,X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(powerset(X5),X6,X7))) = apply(sK5,sK8(X8,sK13(powerset(X5),X6,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_721])]) ).
fof(f4452,plain,
( ! [X8,X6,X7,X5] :
( sP2(powerset(X5),X6,X7)
| ~ empty(X5)
| in(sK13(powerset(X5),X6,X7),X7)
| sP0(X8,sK13(powerset(X5),X6,X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(powerset(X5),X6,X7))) = apply(sK5,sK8(X8,sK13(powerset(X5),X6,X7))) )
| ~ spl22_212
| ~ spl22_373 ),
inference(resolution,[],[f4165,f2090]) ).
fof(f11565,plain,
( spl22_720
| ~ spl22_212
| ~ spl22_371 ),
inference(avatar_split_clause,[],[f4401,f4156,f2089,f11563]) ).
fof(f11563,plain,
( spl22_720
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,powerset(X7))
| ~ empty(X7)
| in(sK13(X5,X6,powerset(X7)),X5)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_720])]) ).
fof(f4401,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,powerset(X7))
| ~ empty(X7)
| in(sK13(X5,X6,powerset(X7)),X5)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) )
| ~ spl22_212
| ~ spl22_371 ),
inference(resolution,[],[f4157,f2090]) ).
fof(f11561,plain,
( spl22_719
| ~ spl22_212
| ~ spl22_369 ),
inference(avatar_split_clause,[],[f4350,f4148,f2089,f11559]) ).
fof(f11559,plain,
( spl22_719
<=> ! [X5,X7,X6,X8] :
( sP2(X5,powerset(X6),X7)
| ~ empty(X6)
| in(sK13(X5,powerset(X6),X7),X7)
| sP0(X8,sK13(X5,powerset(X6),X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,powerset(X6),X7))) = apply(sK5,sK8(X8,sK13(X5,powerset(X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_719])]) ).
fof(f4350,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,powerset(X6),X7)
| ~ empty(X6)
| in(sK13(X5,powerset(X6),X7),X7)
| sP0(X8,sK13(X5,powerset(X6),X7))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,powerset(X6),X7))) = apply(sK5,sK8(X8,sK13(X5,powerset(X6),X7))) )
| ~ spl22_212
| ~ spl22_369 ),
inference(resolution,[],[f4149,f2090]) ).
fof(f11557,plain,
( spl22_718
| ~ spl22_212
| ~ spl22_367 ),
inference(avatar_split_clause,[],[f4299,f4139,f2089,f11555]) ).
fof(f11555,plain,
( spl22_718
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,powerset(X7))
| ~ empty(X7)
| in(sK13(X5,X6,powerset(X7)),X6)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_718])]) ).
fof(f4299,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,powerset(X7))
| ~ empty(X7)
| in(sK13(X5,X6,powerset(X7)),X6)
| sP0(X8,sK13(X5,X6,powerset(X7)))
| apply(relation_dom_restriction(sK5,relation_dom(X8)),sK8(X8,sK13(X5,X6,powerset(X7)))) = apply(sK5,sK8(X8,sK13(X5,X6,powerset(X7)))) )
| ~ spl22_212
| ~ spl22_367 ),
inference(resolution,[],[f4140,f2090]) ).
fof(f11469,plain,
( spl22_717
| ~ spl22_228
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3917,f3857,f2256,f11467]) ).
fof(f11467,plain,
( spl22_717
<=> ! [X75,X77,X78,X76] :
( sP0(X75,powerset(X76))
| ~ empty(X76)
| in(sK8(X75,powerset(X76)),relation_dom(X75))
| sP2(sK7(X75,powerset(X76)),X77,X78)
| apply(relation_dom_restriction(sK5,X78),sK13(sK7(X75,powerset(X76)),X77,X78)) = apply(sK5,sK13(sK7(X75,powerset(X76)),X77,X78)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_717])]) ).
fof(f3917,plain,
( ! [X78,X76,X77,X75] :
( sP0(X75,powerset(X76))
| ~ empty(X76)
| in(sK8(X75,powerset(X76)),relation_dom(X75))
| sP2(sK7(X75,powerset(X76)),X77,X78)
| apply(relation_dom_restriction(sK5,X78),sK13(sK7(X75,powerset(X76)),X77,X78)) = apply(sK5,sK13(sK7(X75,powerset(X76)),X77,X78)) )
| ~ spl22_228
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2257]) ).
fof(f11465,plain,
( spl22_715
| spl22_716
| ~ spl22_65
| ~ spl22_522 ),
inference(avatar_split_clause,[],[f7317,f7174,f610,f11463,f11460]) ).
fof(f11463,plain,
( spl22_716
<=> ! [X0] :
( ~ sP0(sK5,powerset(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_716])]) ).
fof(f7174,plain,
( spl22_522
<=> ! [X3] :
( ~ sP0(sK5,X3)
| element(apply(sK5,sK4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_522])]) ).
fof(f7317,plain,
( ! [X0,X1] :
( ~ sP0(sK5,powerset(X0))
| ~ empty(X0)
| ~ in(X1,apply(sK5,sK4)) )
| ~ spl22_65
| ~ spl22_522 ),
inference(resolution,[],[f7175,f611]) ).
fof(f7175,plain,
( ! [X3] :
( element(apply(sK5,sK4),X3)
| ~ sP0(sK5,X3) )
| ~ spl22_522 ),
inference(avatar_component_clause,[],[f7174]) ).
fof(f11458,plain,
( spl22_714
| ~ spl22_225
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3913,f3857,f2222,f11456]) ).
fof(f11456,plain,
( spl22_714
<=> ! [X61,X60,X59,X62] :
( sP0(X59,powerset(X60))
| ~ empty(X60)
| in(sK8(X59,powerset(X60)),relation_dom(X59))
| sP2(X61,sK7(X59,powerset(X60)),X62)
| apply(relation_dom_restriction(sK5,X62),sK13(X61,sK7(X59,powerset(X60)),X62)) = apply(sK5,sK13(X61,sK7(X59,powerset(X60)),X62)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_714])]) ).
fof(f3913,plain,
( ! [X59,X62,X60,X61] :
( sP0(X59,powerset(X60))
| ~ empty(X60)
| in(sK8(X59,powerset(X60)),relation_dom(X59))
| sP2(X61,sK7(X59,powerset(X60)),X62)
| apply(relation_dom_restriction(sK5,X62),sK13(X61,sK7(X59,powerset(X60)),X62)) = apply(sK5,sK13(X61,sK7(X59,powerset(X60)),X62)) )
| ~ spl22_225
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2223]) ).
fof(f11454,plain,
( spl22_713
| ~ spl22_229
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3912,f3857,f2271,f11452]) ).
fof(f11452,plain,
( spl22_713
<=> ! [X55,X57,X56,X58] :
( sP0(X55,powerset(X56))
| ~ empty(X56)
| in(sK8(X55,powerset(X56)),relation_dom(X55))
| sP2(X57,X58,sK7(X55,powerset(X56)))
| apply(sK5,sK13(X57,X58,sK7(X55,powerset(X56)))) = apply(relation_dom_restriction(sK5,X57),sK13(X57,X58,sK7(X55,powerset(X56)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_713])]) ).
fof(f3912,plain,
( ! [X58,X56,X57,X55] :
( sP0(X55,powerset(X56))
| ~ empty(X56)
| in(sK8(X55,powerset(X56)),relation_dom(X55))
| sP2(X57,X58,sK7(X55,powerset(X56)))
| apply(sK5,sK13(X57,X58,sK7(X55,powerset(X56)))) = apply(relation_dom_restriction(sK5,X57),sK13(X57,X58,sK7(X55,powerset(X56)))) )
| ~ spl22_229
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2272]) ).
fof(f11450,plain,
( spl22_712
| ~ spl22_226
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3911,f3857,f2237,f11448]) ).
fof(f11448,plain,
( spl22_712
<=> ! [X51,X54,X53,X52] :
( sP0(X51,powerset(X52))
| ~ empty(X52)
| in(sK8(X51,powerset(X52)),relation_dom(X51))
| sP2(X53,X54,sK7(X51,powerset(X52)))
| apply(sK5,sK13(X53,X54,sK7(X51,powerset(X52)))) = apply(relation_dom_restriction(sK5,X54),sK13(X53,X54,sK7(X51,powerset(X52)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_712])]) ).
fof(f3911,plain,
( ! [X51,X54,X52,X53] :
( sP0(X51,powerset(X52))
| ~ empty(X52)
| in(sK8(X51,powerset(X52)),relation_dom(X51))
| sP2(X53,X54,sK7(X51,powerset(X52)))
| apply(sK5,sK13(X53,X54,sK7(X51,powerset(X52)))) = apply(relation_dom_restriction(sK5,X54),sK13(X53,X54,sK7(X51,powerset(X52)))) )
| ~ spl22_226
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2238]) ).
fof(f11446,plain,
( spl22_711
| ~ spl22_230
| ~ spl22_301 ),
inference(avatar_split_clause,[],[f3241,f3225,f2286,f11444]) ).
fof(f11444,plain,
( spl22_711
<=> ! [X4,X5,X3] :
( ~ in(X3,relation_dom(X4))
| element(apply(X4,X3),X5)
| sK7(X4,sK10(powerset(X5))) = apply(X4,sK8(X4,sK10(powerset(X5))))
| apply(relation_dom_restriction(sK5,sK10(powerset(X5))),sK7(X4,sK10(powerset(X5)))) = apply(sK5,sK7(X4,sK10(powerset(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_711])]) ).
fof(f3225,plain,
( spl22_301
<=> ! [X18,X16,X17] :
( ~ in(X16,relation_dom(X17))
| ~ sP0(X17,sK10(powerset(X18)))
| element(apply(X17,X16),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_301])]) ).
fof(f3241,plain,
( ! [X3,X4,X5] :
( ~ in(X3,relation_dom(X4))
| element(apply(X4,X3),X5)
| sK7(X4,sK10(powerset(X5))) = apply(X4,sK8(X4,sK10(powerset(X5))))
| apply(relation_dom_restriction(sK5,sK10(powerset(X5))),sK7(X4,sK10(powerset(X5)))) = apply(sK5,sK7(X4,sK10(powerset(X5)))) )
| ~ spl22_230
| ~ spl22_301 ),
inference(resolution,[],[f3226,f2287]) ).
fof(f3226,plain,
( ! [X18,X16,X17] :
( ~ sP0(X17,sK10(powerset(X18)))
| ~ in(X16,relation_dom(X17))
| element(apply(X17,X16),X18) )
| ~ spl22_301 ),
inference(avatar_component_clause,[],[f3225]) ).
fof(f10809,plain,
( spl22_710
| ~ spl22_145
| ~ spl22_317 ),
inference(avatar_split_clause,[],[f3595,f3335,f1312,f10807]) ).
fof(f10807,plain,
( spl22_710
<=> ! [X2,X1] :
( ~ in(sK13(X1,X2,X2),X1)
| sP2(X1,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_710])]) ).
fof(f3335,plain,
( spl22_317
<=> ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(sK13(X0,X1,X1),X0)
| ~ in(sK13(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_317])]) ).
fof(f3595,plain,
( ! [X2,X1] :
( ~ in(sK13(X1,X2,X2),X1)
| sP2(X1,X2,X2) )
| ~ spl22_145
| ~ spl22_317 ),
inference(duplicate_literal_removal,[],[f3547]) ).
fof(f3547,plain,
( ! [X2,X1] :
( ~ in(sK13(X1,X2,X2),X1)
| sP2(X1,X2,X2)
| sP2(X1,X2,X2) )
| ~ spl22_145
| ~ spl22_317 ),
inference(resolution,[],[f3336,f1313]) ).
fof(f3336,plain,
( ! [X0,X1] :
( ~ in(sK13(X0,X1,X1),X1)
| ~ in(sK13(X0,X1,X1),X0)
| sP2(X0,X1,X1) )
| ~ spl22_317 ),
inference(avatar_component_clause,[],[f3335]) ).
fof(f10805,plain,
( spl22_709
| ~ spl22_236
| ~ spl22_306 ),
inference(avatar_split_clause,[],[f3277,f3256,f2331,f10803]) ).
fof(f10803,plain,
( spl22_709
<=> ! [X6,X7] :
( ~ empty(X6)
| sP0(X7,sK10(powerset(X6)))
| ~ sP0(X7,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_709])]) ).
fof(f3277,plain,
( ! [X6,X7] :
( ~ empty(X6)
| sP0(X7,sK10(powerset(X6)))
| ~ sP0(X7,sK15) )
| ~ spl22_236
| ~ spl22_306 ),
inference(resolution,[],[f3257,f2332]) ).
fof(f10801,plain,
( spl22_708
| ~ spl22_41
| ~ spl22_278 ),
inference(avatar_split_clause,[],[f2984,f2959,f414,f10799]) ).
fof(f2984,plain,
( ! [X8,X6,X7] :
( ~ in(X6,X7)
| ~ in(X6,X8)
| ~ empty(set_intersection2(X7,X8)) )
| ~ spl22_41
| ~ spl22_278 ),
inference(resolution,[],[f2960,f415]) ).
fof(f10797,plain,
( spl22_707
| ~ spl22_56
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f2875,f2719,f540,f10795]) ).
fof(f10795,plain,
( spl22_707
<=> ! [X5] :
( empty(X5)
| empty(sK6(X5))
| in(sK10(sK6(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_707])]) ).
fof(f2875,plain,
( ! [X5] :
( empty(X5)
| empty(sK6(X5))
| in(sK10(sK6(X5)),X5) )
| ~ spl22_56
| ~ spl22_257 ),
inference(duplicate_literal_removal,[],[f2874]) ).
fof(f2874,plain,
( ! [X5] :
( empty(X5)
| empty(sK6(X5))
| empty(X5)
| in(sK10(sK6(X5)),X5) )
| ~ spl22_56
| ~ spl22_257 ),
inference(resolution,[],[f2720,f541]) ).
fof(f10793,plain,
( spl22_706
| ~ spl22_250
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2860,f2711,f2571,f10791]) ).
fof(f10791,plain,
( spl22_706
<=> ! [X22,X20,X21] :
( sP2(sK15,X20,relation_dom(X21))
| ~ sP0(X21,X22)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_706])]) ).
fof(f2860,plain,
( ! [X21,X22,X20] :
( sP2(sK15,X20,relation_dom(X21))
| ~ sP0(X21,X22)
| ~ empty(X22) )
| ~ spl22_250
| ~ spl22_255 ),
inference(resolution,[],[f2712,f2572]) ).
fof(f10789,plain,
( spl22_705
| ~ spl22_45
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2856,f2711,f448,f10787]) ).
fof(f10787,plain,
( spl22_705
<=> ! [X9,X10] :
( sP2(sK15,X9,X10)
| ~ in(X10,sK13(sK15,X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_705])]) ).
fof(f2856,plain,
( ! [X10,X9] :
( sP2(sK15,X9,X10)
| ~ in(X10,sK13(sK15,X9,X10)) )
| ~ spl22_45
| ~ spl22_255 ),
inference(resolution,[],[f2712,f449]) ).
fof(f10767,plain,
( spl22_704
| ~ spl22_250
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2845,f2707,f2571,f10765]) ).
fof(f10765,plain,
( spl22_704
<=> ! [X22,X20,X21] :
( sP2(X20,sK15,relation_dom(X21))
| ~ sP0(X21,X22)
| ~ empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_704])]) ).
fof(f2845,plain,
( ! [X21,X22,X20] :
( sP2(X20,sK15,relation_dom(X21))
| ~ sP0(X21,X22)
| ~ empty(X22) )
| ~ spl22_250
| ~ spl22_254 ),
inference(resolution,[],[f2708,f2572]) ).
fof(f10763,plain,
( spl22_703
| ~ spl22_45
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2841,f2707,f448,f10761]) ).
fof(f10761,plain,
( spl22_703
<=> ! [X9,X10] :
( sP2(X9,sK15,X10)
| ~ in(X10,sK13(X9,sK15,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_703])]) ).
fof(f2841,plain,
( ! [X10,X9] :
( sP2(X9,sK15,X10)
| ~ in(X10,sK13(X9,sK15,X10)) )
| ~ spl22_45
| ~ spl22_254 ),
inference(resolution,[],[f2708,f449]) ).
fof(f10759,plain,
( spl22_702
| ~ spl22_250
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2825,f2703,f2571,f10757]) ).
fof(f10757,plain,
( spl22_702
<=> ! [X20,X21,X19] :
( sP2(X19,relation_dom(X20),sK15)
| ~ sP0(X20,X21)
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_702])]) ).
fof(f2825,plain,
( ! [X21,X19,X20] :
( sP2(X19,relation_dom(X20),sK15)
| ~ sP0(X20,X21)
| ~ empty(X21) )
| ~ spl22_250
| ~ spl22_253 ),
inference(resolution,[],[f2704,f2572]) ).
fof(f10755,plain,
( spl22_701
| ~ spl22_45
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2821,f2703,f448,f10753]) ).
fof(f10753,plain,
( spl22_701
<=> ! [X9,X8] :
( sP2(X8,X9,sK15)
| ~ in(X9,sK13(X8,X9,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_701])]) ).
fof(f2821,plain,
( ! [X8,X9] :
( sP2(X8,X9,sK15)
| ~ in(X9,sK13(X8,X9,sK15)) )
| ~ spl22_45
| ~ spl22_253 ),
inference(resolution,[],[f2704,f449]) ).
fof(f10751,plain,
( spl22_700
| ~ spl22_250
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2810,f2699,f2571,f10749]) ).
fof(f10749,plain,
( spl22_700
<=> ! [X20,X21,X19] :
( sP2(relation_dom(X19),X20,sK15)
| ~ sP0(X19,X21)
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_700])]) ).
fof(f2810,plain,
( ! [X21,X19,X20] :
( sP2(relation_dom(X19),X20,sK15)
| ~ sP0(X19,X21)
| ~ empty(X21) )
| ~ spl22_250
| ~ spl22_252 ),
inference(resolution,[],[f2700,f2572]) ).
fof(f10747,plain,
( spl22_699
| ~ spl22_45
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2806,f2699,f448,f10745]) ).
fof(f10745,plain,
( spl22_699
<=> ! [X9,X8] :
( sP2(X8,X9,sK15)
| ~ in(X8,sK13(X8,X9,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_699])]) ).
fof(f2806,plain,
( ! [X8,X9] :
( sP2(X8,X9,sK15)
| ~ in(X8,sK13(X8,X9,sK15)) )
| ~ spl22_45
| ~ spl22_252 ),
inference(resolution,[],[f2700,f449]) ).
fof(f10743,plain,
( spl22_698
| ~ spl22_150
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2676,f2571,f1366,f10741]) ).
fof(f10741,plain,
( spl22_698
<=> ! [X27,X28,X26] :
( ~ sP0(X26,X27)
| ~ empty(X27)
| sP0(X26,X28)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_698])]) ).
fof(f1366,plain,
( spl22_150
<=> ! [X4,X5] :
( in(sK8(X4,X5),relation_dom(X4))
| sP0(X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_150])]) ).
fof(f2676,plain,
( ! [X28,X26,X27] :
( ~ sP0(X26,X27)
| ~ empty(X27)
| sP0(X26,X28)
| ~ empty(X28) )
| ~ spl22_150
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1367]) ).
fof(f1367,plain,
( ! [X4,X5] :
( in(sK8(X4,X5),relation_dom(X4))
| sP0(X4,X5)
| ~ empty(X5) )
| ~ spl22_150 ),
inference(avatar_component_clause,[],[f1366]) ).
fof(f10739,plain,
( spl22_697
| ~ spl22_36
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f2646,f2567,f393,f10737]) ).
fof(f10737,plain,
( spl22_697
<=> ! [X2,X3] :
( relation_dom(relation_dom(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_697])]) ).
fof(f2646,plain,
( ! [X2,X3] :
( relation_dom(relation_dom(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) )
| ~ spl22_36
| ~ spl22_249 ),
inference(resolution,[],[f2568,f394]) ).
fof(f10735,plain,
( spl22_696
| ~ spl22_34
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f2645,f2567,f385,f10733]) ).
fof(f10733,plain,
( spl22_696
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_696])]) ).
fof(f385,plain,
( spl22_34
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_34])]) ).
fof(f2645,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_249 ),
inference(resolution,[],[f2568,f386]) ).
fof(f386,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f10731,plain,
( spl22_695
| ~ spl22_36
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2624,f2563,f393,f10729]) ).
fof(f10729,plain,
( spl22_695
<=> ! [X2,X3] :
( relation_dom(relation_rng(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_695])]) ).
fof(f2624,plain,
( ! [X2,X3] :
( relation_dom(relation_rng(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) )
| ~ spl22_36
| ~ spl22_248 ),
inference(resolution,[],[f2564,f394]) ).
fof(f10709,plain,
( spl22_694
| ~ spl22_34
| ~ spl22_248 ),
inference(avatar_split_clause,[],[f2623,f2563,f385,f10707]) ).
fof(f10707,plain,
( spl22_694
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_694])]) ).
fof(f2623,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_248 ),
inference(resolution,[],[f2564,f386]) ).
fof(f10705,plain,
( spl22_693
| ~ spl22_36
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f2602,f2559,f393,f10703]) ).
fof(f10703,plain,
( spl22_693
<=> ! [X2,X3] :
( relation_rng(relation_dom(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_693])]) ).
fof(f2602,plain,
( ! [X2,X3] :
( relation_rng(relation_dom(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) )
| ~ spl22_36
| ~ spl22_247 ),
inference(resolution,[],[f2560,f394]) ).
fof(f10701,plain,
( spl22_692
| ~ spl22_34
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f2601,f2559,f385,f10699]) ).
fof(f10699,plain,
( spl22_692
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_692])]) ).
fof(f2601,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_247 ),
inference(resolution,[],[f2560,f386]) ).
fof(f10697,plain,
( spl22_691
| ~ spl22_36
| ~ spl22_246 ),
inference(avatar_split_clause,[],[f2575,f2555,f393,f10695]) ).
fof(f10695,plain,
( spl22_691
<=> ! [X2,X3] :
( relation_rng(relation_rng(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_691])]) ).
fof(f2575,plain,
( ! [X2,X3] :
( relation_rng(relation_rng(relation_dom(X2))) = X3
| ~ empty(X3)
| ~ empty(X2) )
| ~ spl22_36
| ~ spl22_246 ),
inference(resolution,[],[f2556,f394]) ).
fof(f10693,plain,
( spl22_690
| ~ spl22_34
| ~ spl22_246 ),
inference(avatar_split_clause,[],[f2574,f2555,f385,f10691]) ).
fof(f10691,plain,
( spl22_690
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_690])]) ).
fof(f2574,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_246 ),
inference(resolution,[],[f2556,f386]) ).
fof(f10689,plain,
( spl22_689
| ~ spl22_124
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2508,f2439,f1103,f10687]) ).
fof(f10687,plain,
( spl22_689
<=> ! [X20,X19] :
( in(sK10(set_intersection2(X19,X20)),X19)
| empty(set_intersection2(X19,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_689])]) ).
fof(f2508,plain,
( ! [X19,X20] :
( in(sK10(set_intersection2(X19,X20)),X19)
| empty(set_intersection2(X19,X20)) )
| ~ spl22_124
| ~ spl22_238 ),
inference(resolution,[],[f2440,f1104]) ).
fof(f10685,plain,
( spl22_688
| ~ spl22_124
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2477,f2435,f1103,f10683]) ).
fof(f10683,plain,
( spl22_688
<=> ! [X20,X19] :
( in(sK10(set_intersection2(X19,X20)),X20)
| empty(set_intersection2(X19,X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_688])]) ).
fof(f2477,plain,
( ! [X19,X20] :
( in(sK10(set_intersection2(X19,X20)),X20)
| empty(set_intersection2(X19,X20)) )
| ~ spl22_124
| ~ spl22_237 ),
inference(resolution,[],[f2436,f1104]) ).
fof(f10681,plain,
( spl22_687
| ~ spl22_156
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2429,f2331,f1407,f10679]) ).
fof(f10679,plain,
( spl22_687
<=> ! [X66,X64,X65] :
( ~ sP0(X64,sK15)
| sP2(relation_dom(X64),X65,X66)
| ~ empty(X66) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_687])]) ).
fof(f2429,plain,
( ! [X65,X66,X64] :
( ~ sP0(X64,sK15)
| sP2(relation_dom(X64),X65,X66)
| ~ empty(X66) )
| ~ spl22_156
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1408]) ).
fof(f10677,plain,
( spl22_686
| ~ spl22_154
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2425,f2331,f1399,f10675]) ).
fof(f10675,plain,
( spl22_686
<=> ! [X54,X52,X53] :
( ~ sP0(X52,sK15)
| sP2(X53,relation_dom(X52),X54)
| ~ empty(X54) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_686])]) ).
fof(f2425,plain,
( ! [X54,X52,X53] :
( ~ sP0(X52,sK15)
| sP2(X53,relation_dom(X52),X54)
| ~ empty(X54) )
| ~ spl22_154
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1400]) ).
fof(f10673,plain,
( spl22_685
| ~ spl22_157
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2418,f2331,f1411,f10671]) ).
fof(f10671,plain,
( spl22_685
<=> ! [X32,X33,X31] :
( ~ sP0(X31,sK15)
| sP2(X32,X33,relation_dom(X31))
| ~ empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_685])]) ).
fof(f2418,plain,
( ! [X31,X32,X33] :
( ~ sP0(X31,sK15)
| sP2(X32,X33,relation_dom(X31))
| ~ empty(X32) )
| ~ spl22_157
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1412]) ).
fof(f10657,plain,
( spl22_684
| ~ spl22_155
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2417,f2331,f1403,f10655]) ).
fof(f10655,plain,
( spl22_684
<=> ! [X29,X28,X30] :
( ~ sP0(X28,sK15)
| sP2(X29,X30,relation_dom(X28))
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_684])]) ).
fof(f2417,plain,
( ! [X28,X29,X30] :
( ~ sP0(X28,sK15)
| sP2(X29,X30,relation_dom(X28))
| ~ empty(X30) )
| ~ spl22_155
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1404]) ).
fof(f10653,plain,
( spl22_683
| ~ spl22_149
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2407,f2331,f1362,f10651]) ).
fof(f10651,plain,
( spl22_683
<=> ! [X7,X8] :
( ~ sP0(X7,sK15)
| sP0(X8,relation_dom(X7))
| ~ empty(relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_683])]) ).
fof(f2407,plain,
( ! [X8,X7] :
( ~ sP0(X7,sK15)
| sP0(X8,relation_dom(X7))
| ~ empty(relation_dom(X8)) )
| ~ spl22_149
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1363]) ).
fof(f10649,plain,
( spl22_682
| ~ spl22_135
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2186,f2120,f1205,f10647]) ).
fof(f10647,plain,
( spl22_682
<=> ! [X9,X10] :
( ~ empty(X9)
| ~ empty(X10)
| relation_dom(sK10(powerset(X9))) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_682])]) ).
fof(f1205,plain,
( spl22_135
<=> ! [X2,X3] :
( relation_dom(X3) = X2
| ~ empty(X2)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_135])]) ).
fof(f2186,plain,
( ! [X10,X9] :
( ~ empty(X9)
| ~ empty(X10)
| relation_dom(sK10(powerset(X9))) = X10 )
| ~ spl22_135
| ~ spl22_216 ),
inference(resolution,[],[f2121,f1206]) ).
fof(f1206,plain,
( ! [X2,X3] :
( ~ empty(X3)
| ~ empty(X2)
| relation_dom(X3) = X2 )
| ~ spl22_135 ),
inference(avatar_component_clause,[],[f1205]) ).
fof(f10645,plain,
( spl22_681
| ~ spl22_134
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2185,f2120,f1198,f10643]) ).
fof(f10643,plain,
( spl22_681
<=> ! [X7,X8] :
( ~ empty(X7)
| ~ empty(X8)
| relation_rng(sK10(powerset(X7))) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_681])]) ).
fof(f1198,plain,
( spl22_134
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_134])]) ).
fof(f2185,plain,
( ! [X8,X7] :
( ~ empty(X7)
| ~ empty(X8)
| relation_rng(sK10(powerset(X7))) = X8 )
| ~ spl22_134
| ~ spl22_216 ),
inference(resolution,[],[f2121,f1199]) ).
fof(f1199,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl22_134 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f10620,plain,
( spl22_680
| ~ spl22_213
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5236,f5075,f2102,f10618]) ).
fof(f10618,plain,
( spl22_680
<=> ! [X55,X54,X56,X57] :
( ~ sP0(X54,X55)
| apply(relation_dom_restriction(X56,X55),apply(X54,sK8(X54,X57))) = apply(X56,apply(X54,sK8(X54,X57)))
| ~ function(X56)
| ~ relation(X56)
| sP0(X54,X57)
| apply(relation_dom_restriction(sK5,X57),sK7(X54,X57)) = apply(sK5,sK7(X54,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_680])]) ).
fof(f5236,plain,
( ! [X56,X54,X57,X55] :
( ~ sP0(X54,X55)
| apply(relation_dom_restriction(X56,X55),apply(X54,sK8(X54,X57))) = apply(X56,apply(X54,sK8(X54,X57)))
| ~ function(X56)
| ~ relation(X56)
| sP0(X54,X57)
| apply(relation_dom_restriction(sK5,X57),sK7(X54,X57)) = apply(sK5,sK7(X54,X57)) )
| ~ spl22_213
| ~ spl22_396 ),
inference(resolution,[],[f5076,f2103]) ).
fof(f10561,plain,
( spl22_679
| ~ spl22_212
| ~ spl22_350 ),
inference(avatar_split_clause,[],[f3897,f3857,f2089,f10559]) ).
fof(f10559,plain,
( spl22_679
<=> ! [X6,X4,X5] :
( sP0(X4,powerset(X5))
| ~ empty(X5)
| in(sK8(X4,powerset(X5)),relation_dom(X4))
| sP0(X6,sK7(X4,powerset(X5)))
| apply(relation_dom_restriction(sK5,relation_dom(X6)),sK8(X6,sK7(X4,powerset(X5)))) = apply(sK5,sK8(X6,sK7(X4,powerset(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_679])]) ).
fof(f3897,plain,
( ! [X6,X4,X5] :
( sP0(X4,powerset(X5))
| ~ empty(X5)
| in(sK8(X4,powerset(X5)),relation_dom(X4))
| sP0(X6,sK7(X4,powerset(X5)))
| apply(relation_dom_restriction(sK5,relation_dom(X6)),sK8(X6,sK7(X4,powerset(X5)))) = apply(sK5,sK8(X6,sK7(X4,powerset(X5)))) )
| ~ spl22_212
| ~ spl22_350 ),
inference(resolution,[],[f3858,f2090]) ).
fof(f10557,plain,
( spl22_678
| ~ spl22_228
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3213,f3185,f2256,f10555]) ).
fof(f10555,plain,
( spl22_678
<=> ! [X54,X55,X56] :
( ~ sP1(X54)
| sK13(relation_rng(X54),X55,X56) = apply(X54,sK9(X54,sK13(relation_rng(X54),X55,X56)))
| sP2(relation_rng(X54),X55,X56)
| apply(relation_dom_restriction(sK5,X56),sK13(relation_rng(X54),X55,X56)) = apply(sK5,sK13(relation_rng(X54),X55,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_678])]) ).
fof(f3213,plain,
( ! [X56,X54,X55] :
( ~ sP1(X54)
| sK13(relation_rng(X54),X55,X56) = apply(X54,sK9(X54,sK13(relation_rng(X54),X55,X56)))
| sP2(relation_rng(X54),X55,X56)
| apply(relation_dom_restriction(sK5,X56),sK13(relation_rng(X54),X55,X56)) = apply(sK5,sK13(relation_rng(X54),X55,X56)) )
| ~ spl22_228
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2257]) ).
fof(f10553,plain,
( spl22_677
| ~ spl22_225
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3209,f3185,f2222,f10551]) ).
fof(f10551,plain,
( spl22_677
<=> ! [X44,X43,X42] :
( ~ sP1(X42)
| sK13(X43,relation_rng(X42),X44) = apply(X42,sK9(X42,sK13(X43,relation_rng(X42),X44)))
| sP2(X43,relation_rng(X42),X44)
| apply(relation_dom_restriction(sK5,X44),sK13(X43,relation_rng(X42),X44)) = apply(sK5,sK13(X43,relation_rng(X42),X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_677])]) ).
fof(f3209,plain,
( ! [X44,X42,X43] :
( ~ sP1(X42)
| sK13(X43,relation_rng(X42),X44) = apply(X42,sK9(X42,sK13(X43,relation_rng(X42),X44)))
| sP2(X43,relation_rng(X42),X44)
| apply(relation_dom_restriction(sK5,X44),sK13(X43,relation_rng(X42),X44)) = apply(sK5,sK13(X43,relation_rng(X42),X44)) )
| ~ spl22_225
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2223]) ).
fof(f10549,plain,
( spl22_676
| ~ spl22_229
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3208,f3185,f2271,f10547]) ).
fof(f10547,plain,
( spl22_676
<=> ! [X41,X40,X39] :
( ~ sP1(X39)
| sK13(X40,X41,relation_rng(X39)) = apply(X39,sK9(X39,sK13(X40,X41,relation_rng(X39))))
| sP2(X40,X41,relation_rng(X39))
| apply(sK5,sK13(X40,X41,relation_rng(X39))) = apply(relation_dom_restriction(sK5,X40),sK13(X40,X41,relation_rng(X39))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_676])]) ).
fof(f3208,plain,
( ! [X40,X41,X39] :
( ~ sP1(X39)
| sK13(X40,X41,relation_rng(X39)) = apply(X39,sK9(X39,sK13(X40,X41,relation_rng(X39))))
| sP2(X40,X41,relation_rng(X39))
| apply(sK5,sK13(X40,X41,relation_rng(X39))) = apply(relation_dom_restriction(sK5,X40),sK13(X40,X41,relation_rng(X39))) )
| ~ spl22_229
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2272]) ).
fof(f10545,plain,
( spl22_675
| ~ spl22_226
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3207,f3185,f2237,f10543]) ).
fof(f10543,plain,
( spl22_675
<=> ! [X38,X36,X37] :
( ~ sP1(X36)
| sK13(X37,X38,relation_rng(X36)) = apply(X36,sK9(X36,sK13(X37,X38,relation_rng(X36))))
| sP2(X37,X38,relation_rng(X36))
| apply(sK5,sK13(X37,X38,relation_rng(X36))) = apply(relation_dom_restriction(sK5,X38),sK13(X37,X38,relation_rng(X36))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_675])]) ).
fof(f3207,plain,
( ! [X38,X36,X37] :
( ~ sP1(X36)
| sK13(X37,X38,relation_rng(X36)) = apply(X36,sK9(X36,sK13(X37,X38,relation_rng(X36))))
| sP2(X37,X38,relation_rng(X36))
| apply(sK5,sK13(X37,X38,relation_rng(X36))) = apply(relation_dom_restriction(sK5,X38),sK13(X37,X38,relation_rng(X36))) )
| ~ spl22_226
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2238]) ).
fof(f10473,plain,
( spl22_674
| ~ spl22_513
| ~ spl22_661 ),
inference(avatar_split_clause,[],[f10229,f9975,f7070,f10471]) ).
fof(f10471,plain,
( spl22_674
<=> ! [X3] :
( ~ sP1(X3)
| ~ empty(relation_dom(X3))
| ~ sP0(sK5,relation_rng(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_674])]) ).
fof(f9975,plain,
( spl22_661
<=> ! [X9,X8] :
( ~ in(X8,relation_rng(X9))
| ~ sP1(X9)
| ~ empty(relation_dom(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_661])]) ).
fof(f10229,plain,
( ! [X3] :
( ~ sP1(X3)
| ~ empty(relation_dom(X3))
| ~ sP0(sK5,relation_rng(X3)) )
| ~ spl22_513
| ~ spl22_661 ),
inference(resolution,[],[f9976,f7071]) ).
fof(f9976,plain,
( ! [X8,X9] :
( ~ in(X8,relation_rng(X9))
| ~ sP1(X9)
| ~ empty(relation_dom(X9)) )
| ~ spl22_661 ),
inference(avatar_component_clause,[],[f9975]) ).
fof(f10469,plain,
( spl22_673
| ~ spl22_76
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2276,f2271,f684,f10467]) ).
fof(f10467,plain,
( spl22_673
<=> ! [X9,X7,X6,X8] :
( sP2(X6,X7,X8)
| apply(sK5,sK13(X6,X7,X8)) = apply(relation_dom_restriction(sK5,X6),sK13(X6,X7,X8))
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_673])]) ).
fof(f2276,plain,
( ! [X8,X6,X9,X7] :
( sP2(X6,X7,X8)
| apply(sK5,sK13(X6,X7,X8)) = apply(relation_dom_restriction(sK5,X6),sK13(X6,X7,X8))
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) )
| ~ spl22_76
| ~ spl22_229 ),
inference(resolution,[],[f2272,f685]) ).
fof(f10465,plain,
( spl22_672
| ~ spl22_76
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2261,f2256,f684,f10463]) ).
fof(f10463,plain,
( spl22_672
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(sK5,X7),sK13(X5,X6,X7)) = apply(sK5,sK13(X5,X6,X7))
| apply(X8,sK13(X5,X6,X7)) = apply(relation_dom_restriction(X8,X5),sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_672])]) ).
fof(f2261,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(sK5,X7),sK13(X5,X6,X7)) = apply(sK5,sK13(X5,X6,X7))
| apply(X8,sK13(X5,X6,X7)) = apply(relation_dom_restriction(X8,X5),sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) )
| ~ spl22_76
| ~ spl22_228 ),
inference(resolution,[],[f2257,f685]) ).
fof(f10461,plain,
( spl22_671
| ~ spl22_76
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2242,f2237,f684,f10459]) ).
fof(f10459,plain,
( spl22_671
<=> ! [X9,X7,X6,X8] :
( sP2(X6,X7,X8)
| apply(sK5,sK13(X6,X7,X8)) = apply(relation_dom_restriction(sK5,X7),sK13(X6,X7,X8))
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_671])]) ).
fof(f2242,plain,
( ! [X8,X6,X9,X7] :
( sP2(X6,X7,X8)
| apply(sK5,sK13(X6,X7,X8)) = apply(relation_dom_restriction(sK5,X7),sK13(X6,X7,X8))
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) )
| ~ spl22_76
| ~ spl22_226 ),
inference(resolution,[],[f2238,f685]) ).
fof(f10457,plain,
( spl22_670
| ~ spl22_76
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2227,f2222,f684,f10455]) ).
fof(f10455,plain,
( spl22_670
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(sK5,X7),sK13(X5,X6,X7)) = apply(sK5,sK13(X5,X6,X7))
| apply(relation_dom_restriction(X8,X6),sK13(X5,X6,X7)) = apply(X8,sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_670])]) ).
fof(f2227,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(sK5,X7),sK13(X5,X6,X7)) = apply(sK5,sK13(X5,X6,X7))
| apply(relation_dom_restriction(X8,X6),sK13(X5,X6,X7)) = apply(X8,sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) )
| ~ spl22_76
| ~ spl22_225 ),
inference(resolution,[],[f2223,f685]) ).
fof(f10352,plain,
( spl22_669
| ~ spl22_513
| ~ spl22_659 ),
inference(avatar_split_clause,[],[f10151,f9967,f7070,f10350]) ).
fof(f10350,plain,
( spl22_669
<=> ! [X3] :
( ~ sP1(X3)
| ~ sP0(X3,sK15)
| ~ sP0(sK5,relation_rng(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_669])]) ).
fof(f9967,plain,
( spl22_659
<=> ! [X6,X7] :
( ~ in(X6,relation_rng(X7))
| ~ sP1(X7)
| ~ sP0(X7,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_659])]) ).
fof(f10151,plain,
( ! [X3] :
( ~ sP1(X3)
| ~ sP0(X3,sK15)
| ~ sP0(sK5,relation_rng(X3)) )
| ~ spl22_513
| ~ spl22_659 ),
inference(resolution,[],[f9968,f7071]) ).
fof(f9968,plain,
( ! [X6,X7] :
( ~ in(X6,relation_rng(X7))
| ~ sP1(X7)
| ~ sP0(X7,sK15) )
| ~ spl22_659 ),
inference(avatar_component_clause,[],[f9967]) ).
fof(f10348,plain,
( spl22_668
| spl22_663
| spl22_163
| ~ spl22_431 ),
inference(avatar_split_clause,[],[f6081,f6067,f1497,f10311,f10345]) ).
fof(f10345,plain,
( spl22_668
<=> apply(relation_dom_restriction(sK19,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK19,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_668])]) ).
fof(f10311,plain,
( spl22_663
<=> sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) = apply(sK5,sK8(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_663])]) ).
fof(f1497,plain,
( spl22_163
<=> sP0(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_163])]) ).
fof(f6067,plain,
( spl22_431
<=> ! [X27,X26] :
( sP0(X26,X27)
| sK7(X26,X27) = apply(X26,sK8(X26,X27))
| apply(relation_dom_restriction(sK19,X27),sK7(X26,X27)) = apply(sK19,sK7(X26,X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_431])]) ).
fof(f6081,plain,
( sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) = apply(sK5,sK8(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| apply(relation_dom_restriction(sK19,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK19,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| spl22_163
| ~ spl22_431 ),
inference(resolution,[],[f6068,f1499]) ).
fof(f1499,plain,
( ~ sP0(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))
| spl22_163 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f6068,plain,
( ! [X26,X27] :
( sP0(X26,X27)
| sK7(X26,X27) = apply(X26,sK8(X26,X27))
| apply(relation_dom_restriction(sK19,X27),sK7(X26,X27)) = apply(sK19,sK7(X26,X27)) )
| ~ spl22_431 ),
inference(avatar_component_clause,[],[f6067]) ).
fof(f10343,plain,
( spl22_667
| ~ spl22_228
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3132,f3027,f2256,f10341]) ).
fof(f10341,plain,
( spl22_667
<=> ! [X75,X77,X78,X76] :
( ~ sP0(X75,sK13(apply(X75,X76),X77,X78))
| ~ in(X76,relation_dom(X75))
| sP2(apply(X75,X76),X77,X78)
| apply(relation_dom_restriction(sK5,X78),sK13(apply(X75,X76),X77,X78)) = apply(sK5,sK13(apply(X75,X76),X77,X78)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_667])]) ).
fof(f3132,plain,
( ! [X78,X76,X77,X75] :
( ~ sP0(X75,sK13(apply(X75,X76),X77,X78))
| ~ in(X76,relation_dom(X75))
| sP2(apply(X75,X76),X77,X78)
| apply(relation_dom_restriction(sK5,X78),sK13(apply(X75,X76),X77,X78)) = apply(sK5,sK13(apply(X75,X76),X77,X78)) )
| ~ spl22_228
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2257]) ).
fof(f10339,plain,
( spl22_666
| ~ spl22_225
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3128,f3027,f2222,f10337]) ).
fof(f10337,plain,
( spl22_666
<=> ! [X61,X60,X59,X62] :
( ~ sP0(X59,sK13(X60,apply(X59,X61),X62))
| ~ in(X61,relation_dom(X59))
| sP2(X60,apply(X59,X61),X62)
| apply(relation_dom_restriction(sK5,X62),sK13(X60,apply(X59,X61),X62)) = apply(sK5,sK13(X60,apply(X59,X61),X62)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_666])]) ).
fof(f3128,plain,
( ! [X59,X62,X60,X61] :
( ~ sP0(X59,sK13(X60,apply(X59,X61),X62))
| ~ in(X61,relation_dom(X59))
| sP2(X60,apply(X59,X61),X62)
| apply(relation_dom_restriction(sK5,X62),sK13(X60,apply(X59,X61),X62)) = apply(sK5,sK13(X60,apply(X59,X61),X62)) )
| ~ spl22_225
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2223]) ).
fof(f10335,plain,
( spl22_665
| ~ spl22_229
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3127,f3027,f2271,f10333]) ).
fof(f10333,plain,
( spl22_665
<=> ! [X55,X57,X56,X58] :
( ~ sP0(X55,sK13(X56,X57,apply(X55,X58)))
| ~ in(X58,relation_dom(X55))
| sP2(X56,X57,apply(X55,X58))
| apply(sK5,sK13(X56,X57,apply(X55,X58))) = apply(relation_dom_restriction(sK5,X56),sK13(X56,X57,apply(X55,X58))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_665])]) ).
fof(f3127,plain,
( ! [X58,X56,X57,X55] :
( ~ sP0(X55,sK13(X56,X57,apply(X55,X58)))
| ~ in(X58,relation_dom(X55))
| sP2(X56,X57,apply(X55,X58))
| apply(sK5,sK13(X56,X57,apply(X55,X58))) = apply(relation_dom_restriction(sK5,X56),sK13(X56,X57,apply(X55,X58))) )
| ~ spl22_229
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2272]) ).
fof(f10331,plain,
( spl22_664
| ~ spl22_226
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3126,f3027,f2237,f10329]) ).
fof(f10329,plain,
( spl22_664
<=> ! [X51,X54,X53,X52] :
( ~ sP0(X51,sK13(X52,X53,apply(X51,X54)))
| ~ in(X54,relation_dom(X51))
| sP2(X52,X53,apply(X51,X54))
| apply(sK5,sK13(X52,X53,apply(X51,X54))) = apply(relation_dom_restriction(sK5,X53),sK13(X52,X53,apply(X51,X54))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_664])]) ).
fof(f3126,plain,
( ! [X51,X54,X52,X53] :
( ~ sP0(X51,sK13(X52,X53,apply(X51,X54)))
| ~ in(X54,relation_dom(X51))
| sP2(X52,X53,apply(X51,X54))
| apply(sK5,sK13(X52,X53,apply(X51,X54))) = apply(relation_dom_restriction(sK5,X53),sK13(X52,X53,apply(X51,X54))) )
| ~ spl22_226
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2238]) ).
fof(f10314,plain,
( spl22_662
| spl22_663
| spl22_163
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2292,f2286,f1497,f10311,f10307]) ).
fof(f10307,plain,
( spl22_662
<=> apply(relation_dom_restriction(sK5,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK5,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_662])]) ).
fof(f2292,plain,
( sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))) = apply(sK5,sK8(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| apply(relation_dom_restriction(sK5,relation_rng(relation_dom_restriction(sK5,sK3))),sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))) = apply(sK5,sK7(sK5,relation_rng(relation_dom_restriction(sK5,sK3))))
| spl22_163
| ~ spl22_230 ),
inference(resolution,[],[f2287,f1499]) ).
fof(f9977,plain,
( spl22_661
| ~ spl22_41
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3086,f3019,f414,f9975]) ).
fof(f3086,plain,
( ! [X8,X9] :
( ~ in(X8,relation_rng(X9))
| ~ sP1(X9)
| ~ empty(relation_dom(X9)) )
| ~ spl22_41
| ~ spl22_286 ),
inference(resolution,[],[f3020,f415]) ).
fof(f9973,plain,
( spl22_660
| ~ spl22_141
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7086,f7070,f1277,f9971]) ).
fof(f7086,plain,
( ! [X20] :
( ~ sP0(sK5,sK6(X20))
| element(apply(sK5,sK4),X20)
| empty(X20) )
| ~ spl22_141
| ~ spl22_513 ),
inference(resolution,[],[f7071,f1278]) ).
fof(f9969,plain,
( spl22_659
| ~ spl22_236
| ~ spl22_286 ),
inference(avatar_split_clause,[],[f3085,f3019,f2331,f9967]) ).
fof(f3085,plain,
( ! [X6,X7] :
( ~ in(X6,relation_rng(X7))
| ~ sP1(X7)
| ~ sP0(X7,sK15) )
| ~ spl22_236
| ~ spl22_286 ),
inference(resolution,[],[f3020,f2332]) ).
fof(f9965,plain,
( spl22_658
| ~ spl22_64
| ~ spl22_245 ),
inference(avatar_split_clause,[],[f2553,f2468,f606,f9963]) ).
fof(f9963,plain,
( spl22_658
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(X13,X12) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_658])]) ).
fof(f2468,plain,
( spl22_245
<=> ! [X4,X2,X3] :
( sP2(X2,X3,X4)
| ~ empty(X4)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_245])]) ).
fof(f2553,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(X13,X12) = X11 )
| ~ spl22_64
| ~ spl22_245 ),
inference(resolution,[],[f2469,f607]) ).
fof(f2469,plain,
( ! [X2,X3,X4] :
( sP2(X2,X3,X4)
| ~ empty(X4)
| ~ empty(X2) )
| ~ spl22_245 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f9961,plain,
( spl22_657
| ~ spl22_64
| ~ spl22_244 ),
inference(avatar_split_clause,[],[f2549,f2464,f606,f9959]) ).
fof(f9959,plain,
( spl22_657
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(X12,X13) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_657])]) ).
fof(f2464,plain,
( spl22_244
<=> ! [X4,X2,X3] :
( sP2(X2,X3,X4)
| ~ empty(X4)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_244])]) ).
fof(f2549,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| ~ empty(X12)
| set_intersection2(X12,X13) = X11 )
| ~ spl22_64
| ~ spl22_244 ),
inference(resolution,[],[f2465,f607]) ).
fof(f2465,plain,
( ! [X2,X3,X4] :
( sP2(X2,X3,X4)
| ~ empty(X4)
| ~ empty(X3) )
| ~ spl22_244 ),
inference(avatar_component_clause,[],[f2464]) ).
fof(f9957,plain,
( spl22_656
| ~ spl22_146
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2432,f2331,f1316,f9955]) ).
fof(f9955,plain,
( spl22_656
<=> ! [X73,X72] :
( ~ sP0(X72,sK15)
| sP2(relation_dom(X72),X73,relation_dom(X72)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_656])]) ).
fof(f2432,plain,
( ! [X72,X73] :
( ~ sP0(X72,sK15)
| sP2(relation_dom(X72),X73,relation_dom(X72)) )
| ~ spl22_146
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1317]) ).
fof(f9953,plain,
( spl22_655
| ~ spl22_145
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2431,f2331,f1312,f9951]) ).
fof(f9951,plain,
( spl22_655
<=> ! [X70,X71] :
( ~ sP0(X70,sK15)
| sP2(X71,relation_dom(X70),relation_dom(X70)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_655])]) ).
fof(f2431,plain,
( ! [X70,X71] :
( ~ sP0(X70,sK15)
| sP2(X71,relation_dom(X70),relation_dom(X70)) )
| ~ spl22_145
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1313]) ).
fof(f9948,plain,
( spl22_654
| ~ spl22_114
| ~ spl22_122 ),
inference(avatar_split_clause,[],[f9837,f1090,f952,f9945]) ).
fof(f9945,plain,
( spl22_654
<=> sK15 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_654])]) ).
fof(f1090,plain,
( spl22_122
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_122])]) ).
fof(f9837,plain,
( sK15 = sK19
| ~ spl22_114
| ~ spl22_122 ),
inference(resolution,[],[f1091,f953]) ).
fof(f1091,plain,
( empty(sK19)
| ~ spl22_122 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f9833,plain,
( spl22_653
| spl22_122
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f6960,f6919,f1090,f9830]) ).
fof(f9830,plain,
( spl22_653
<=> apply(relation_dom_restriction(sK5,sK19),sK10(sK19)) = apply(sK5,sK10(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_653])]) ).
fof(f6919,plain,
( spl22_498
<=> ! [X11] :
( apply(relation_dom_restriction(sK5,X11),sK10(X11)) = apply(sK5,sK10(X11))
| empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_498])]) ).
fof(f6960,plain,
( apply(relation_dom_restriction(sK5,sK19),sK10(sK19)) = apply(sK5,sK10(sK19))
| spl22_122
| ~ spl22_498 ),
inference(resolution,[],[f6920,f1092]) ).
fof(f1092,plain,
( ~ empty(sK19)
| spl22_122 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f6920,plain,
( ! [X11] :
( empty(X11)
| apply(relation_dom_restriction(sK5,X11),sK10(X11)) = apply(sK5,sK10(X11)) )
| ~ spl22_498 ),
inference(avatar_component_clause,[],[f6919]) ).
fof(f9828,plain,
( spl22_652
| ~ spl22_216
| ~ spl22_235 ),
inference(avatar_split_clause,[],[f2389,f2327,f2120,f9826]) ).
fof(f9826,plain,
( spl22_652
<=> ! [X2] :
( sK15 = relation_dom(relation_dom(sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_652])]) ).
fof(f2327,plain,
( spl22_235
<=> ! [X1] :
( sK15 = relation_dom(relation_dom(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_235])]) ).
fof(f2389,plain,
( ! [X2] :
( sK15 = relation_dom(relation_dom(sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_216
| ~ spl22_235 ),
inference(resolution,[],[f2328,f2121]) ).
fof(f2328,plain,
( ! [X1] :
( ~ empty(X1)
| sK15 = relation_dom(relation_dom(X1)) )
| ~ spl22_235 ),
inference(avatar_component_clause,[],[f2327]) ).
fof(f9824,plain,
( spl22_651
| ~ spl22_216
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f2372,f2306,f2120,f9822]) ).
fof(f9822,plain,
( spl22_651
<=> ! [X2] :
( sK15 = relation_dom(relation_rng(sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_651])]) ).
fof(f2306,plain,
( spl22_234
<=> ! [X0] :
( sK15 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_234])]) ).
fof(f2372,plain,
( ! [X2] :
( sK15 = relation_dom(relation_rng(sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_216
| ~ spl22_234 ),
inference(resolution,[],[f2307,f2121]) ).
fof(f2307,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_dom(relation_rng(X0)) )
| ~ spl22_234 ),
inference(avatar_component_clause,[],[f2306]) ).
fof(f9820,plain,
( spl22_650
| ~ spl22_216
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2355,f2302,f2120,f9818]) ).
fof(f9818,plain,
( spl22_650
<=> ! [X2] :
( sK15 = relation_rng(relation_dom(sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_650])]) ).
fof(f2302,plain,
( spl22_233
<=> ! [X1] :
( sK15 = relation_rng(relation_dom(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_233])]) ).
fof(f2355,plain,
( ! [X2] :
( sK15 = relation_rng(relation_dom(sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_216
| ~ spl22_233 ),
inference(resolution,[],[f2303,f2121]) ).
fof(f2303,plain,
( ! [X1] :
( ~ empty(X1)
| sK15 = relation_rng(relation_dom(X1)) )
| ~ spl22_233 ),
inference(avatar_component_clause,[],[f2302]) ).
fof(f9816,plain,
( spl22_649
| ~ spl22_216
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2338,f2298,f2120,f9814]) ).
fof(f9814,plain,
( spl22_649
<=> ! [X2] :
( sK15 = relation_rng(relation_rng(sK10(powerset(X2))))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_649])]) ).
fof(f2298,plain,
( spl22_232
<=> ! [X0] :
( sK15 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_232])]) ).
fof(f2338,plain,
( ! [X2] :
( sK15 = relation_rng(relation_rng(sK10(powerset(X2))))
| ~ empty(X2) )
| ~ spl22_216
| ~ spl22_232 ),
inference(resolution,[],[f2299,f2121]) ).
fof(f2299,plain,
( ! [X0] :
( ~ empty(X0)
| sK15 = relation_rng(relation_rng(X0)) )
| ~ spl22_232 ),
inference(avatar_component_clause,[],[f2298]) ).
fof(f9812,plain,
( spl22_648
| ~ spl22_54
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2181,f2120,f506,f9810]) ).
fof(f9810,plain,
( spl22_648
<=> ! [X2,X3] :
( ~ empty(X2)
| sK10(powerset(X2)) = X3
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_648])]) ).
fof(f2181,plain,
( ! [X2,X3] :
( ~ empty(X2)
| sK10(powerset(X2)) = X3
| ~ empty(X3) )
| ~ spl22_54
| ~ spl22_216 ),
inference(resolution,[],[f2121,f507]) ).
fof(f9760,plain,
( ~ spl22_91
| ~ spl22_42
| spl22_647
| ~ spl22_112
| ~ spl22_174
| ~ spl22_197 ),
inference(avatar_split_clause,[],[f1975,f1926,f1566,f944,f9758,f433,f795]) ).
fof(f1566,plain,
( spl22_174
<=> ! [X0,X1] :
( relation_dom_restriction(X0,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_174])]) ).
fof(f1975,plain,
( ! [X9] :
( sK15 = relation_dom_restriction(sK15,X9)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_112
| ~ spl22_174
| ~ spl22_197 ),
inference(trivial_inequality_removal,[],[f1974]) ).
fof(f1974,plain,
( ! [X9] :
( sK15 != sK15
| sK15 = relation_dom_restriction(sK15,X9)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_112
| ~ spl22_174
| ~ spl22_197 ),
inference(forward_demodulation,[],[f1966,f945]) ).
fof(f1966,plain,
( ! [X9] :
( sK15 != set_intersection2(sK15,X9)
| sK15 = relation_dom_restriction(sK15,X9)
| ~ function(sK15)
| ~ relation(sK15) )
| ~ spl22_174
| ~ spl22_197 ),
inference(superposition,[],[f1567,f1928]) ).
fof(f1567,plain,
( ! [X0,X1] :
( relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| relation_dom_restriction(X0,X1) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_174 ),
inference(avatar_component_clause,[],[f1566]) ).
fof(f9742,plain,
( spl22_646
| ~ spl22_212
| ~ spl22_299 ),
inference(avatar_split_clause,[],[f3193,f3185,f2089,f9740]) ).
fof(f9740,plain,
( spl22_646
<=> ! [X4,X3] :
( ~ sP1(X3)
| sK7(X4,relation_rng(X3)) = apply(X3,sK9(X3,sK7(X4,relation_rng(X3))))
| sP0(X4,relation_rng(X3))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,relation_rng(X3))) = apply(sK5,sK8(X4,relation_rng(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_646])]) ).
fof(f3193,plain,
( ! [X3,X4] :
( ~ sP1(X3)
| sK7(X4,relation_rng(X3)) = apply(X3,sK9(X3,sK7(X4,relation_rng(X3))))
| sP0(X4,relation_rng(X3))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,relation_rng(X3))) = apply(sK5,sK8(X4,relation_rng(X3))) )
| ~ spl22_212
| ~ spl22_299 ),
inference(resolution,[],[f3186,f2090]) ).
fof(f9719,plain,
( spl22_645
| spl22_11
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f6959,f6919,f269,f9716]) ).
fof(f9716,plain,
( spl22_645
<=> apply(relation_dom_restriction(sK5,sK16),sK10(sK16)) = apply(sK5,sK10(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_645])]) ).
fof(f269,plain,
( spl22_11
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).
fof(f6959,plain,
( apply(relation_dom_restriction(sK5,sK16),sK10(sK16)) = apply(sK5,sK10(sK16))
| spl22_11
| ~ spl22_498 ),
inference(resolution,[],[f6920,f271]) ).
fof(f271,plain,
( ~ empty(sK16)
| spl22_11 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f9674,plain,
( spl22_644
| ~ spl22_212
| ~ spl22_288 ),
inference(avatar_split_clause,[],[f3112,f3027,f2089,f9672]) ).
fof(f9672,plain,
( spl22_644
<=> ! [X6,X4,X5] :
( ~ sP0(X4,sK7(X5,apply(X4,X6)))
| ~ in(X6,relation_dom(X4))
| sP0(X5,apply(X4,X6))
| apply(relation_dom_restriction(sK5,relation_dom(X5)),sK8(X5,apply(X4,X6))) = apply(sK5,sK8(X5,apply(X4,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_644])]) ).
fof(f3112,plain,
( ! [X6,X4,X5] :
( ~ sP0(X4,sK7(X5,apply(X4,X6)))
| ~ in(X6,relation_dom(X4))
| sP0(X5,apply(X4,X6))
| apply(relation_dom_restriction(sK5,relation_dom(X5)),sK8(X5,apply(X4,X6))) = apply(sK5,sK8(X5,apply(X4,X6))) )
| ~ spl22_212
| ~ spl22_288 ),
inference(resolution,[],[f3028,f2090]) ).
fof(f9670,plain,
( spl22_643
| ~ spl22_76
| ~ spl22_213 ),
inference(avatar_split_clause,[],[f2107,f2102,f684,f9668]) ).
fof(f9668,plain,
( spl22_643
<=> ! [X6,X5,X7] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK5,X6),sK7(X5,X6)) = apply(sK5,sK7(X5,X6))
| apply(relation_dom_restriction(X7,relation_dom(X5)),sK8(X5,X6)) = apply(X7,sK8(X5,X6))
| ~ function(X7)
| ~ relation(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_643])]) ).
fof(f2107,plain,
( ! [X6,X7,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK5,X6),sK7(X5,X6)) = apply(sK5,sK7(X5,X6))
| apply(relation_dom_restriction(X7,relation_dom(X5)),sK8(X5,X6)) = apply(X7,sK8(X5,X6))
| ~ function(X7)
| ~ relation(X7) )
| ~ spl22_76
| ~ spl22_213 ),
inference(resolution,[],[f2103,f685]) ).
fof(f9666,plain,
( spl22_642
| ~ spl22_76
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2093,f2089,f684,f9664]) ).
fof(f9664,plain,
( spl22_642
<=> ! [X2,X4,X3] :
( sP0(X2,X3)
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,X3)) = apply(sK5,sK8(X2,X3))
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_642])]) ).
fof(f2093,plain,
( ! [X2,X3,X4] :
( sP0(X2,X3)
| apply(relation_dom_restriction(sK5,relation_dom(X2)),sK8(X2,X3)) = apply(sK5,sK8(X2,X3))
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_76
| ~ spl22_212 ),
inference(resolution,[],[f2090,f685]) ).
fof(f9420,plain,
( spl22_641
| spl22_9
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f6958,f6919,f259,f9417]) ).
fof(f9417,plain,
( spl22_641
<=> apply(relation_dom_restriction(sK5,sK14),sK10(sK14)) = apply(sK5,sK10(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_641])]) ).
fof(f259,plain,
( spl22_9
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).
fof(f6958,plain,
( apply(relation_dom_restriction(sK5,sK14),sK10(sK14)) = apply(sK5,sK10(sK14))
| spl22_9
| ~ spl22_498 ),
inference(resolution,[],[f6920,f261]) ).
fof(f261,plain,
( ~ empty(sK14)
| spl22_9 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f9265,plain,
( spl22_640
| ~ spl22_228
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2521,f2439,f2256,f9263]) ).
fof(f9263,plain,
( spl22_640
<=> ! [X69,X71,X70,X72] :
( in(sK13(set_intersection2(X69,X70),X71,X72),X69)
| sP2(set_intersection2(X69,X70),X71,X72)
| apply(relation_dom_restriction(sK5,X72),sK13(set_intersection2(X69,X70),X71,X72)) = apply(sK5,sK13(set_intersection2(X69,X70),X71,X72)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_640])]) ).
fof(f2521,plain,
( ! [X72,X70,X71,X69] :
( in(sK13(set_intersection2(X69,X70),X71,X72),X69)
| sP2(set_intersection2(X69,X70),X71,X72)
| apply(relation_dom_restriction(sK5,X72),sK13(set_intersection2(X69,X70),X71,X72)) = apply(sK5,sK13(set_intersection2(X69,X70),X71,X72)) )
| ~ spl22_228
| ~ spl22_238 ),
inference(resolution,[],[f2440,f2257]) ).
fof(f9261,plain,
( spl22_639
| ~ spl22_225
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2517,f2439,f2222,f9259]) ).
fof(f9259,plain,
( spl22_639
<=> ! [X55,X54,X53,X56] :
( in(sK13(X53,set_intersection2(X54,X55),X56),X54)
| sP2(X53,set_intersection2(X54,X55),X56)
| apply(relation_dom_restriction(sK5,X56),sK13(X53,set_intersection2(X54,X55),X56)) = apply(sK5,sK13(X53,set_intersection2(X54,X55),X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_639])]) ).
fof(f2517,plain,
( ! [X56,X54,X55,X53] :
( in(sK13(X53,set_intersection2(X54,X55),X56),X54)
| sP2(X53,set_intersection2(X54,X55),X56)
| apply(relation_dom_restriction(sK5,X56),sK13(X53,set_intersection2(X54,X55),X56)) = apply(sK5,sK13(X53,set_intersection2(X54,X55),X56)) )
| ~ spl22_225
| ~ spl22_238 ),
inference(resolution,[],[f2440,f2223]) ).
fof(f9257,plain,
( spl22_638
| ~ spl22_229
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2516,f2439,f2271,f9255]) ).
fof(f9255,plain,
( spl22_638
<=> ! [X51,X50,X49,X52] :
( in(sK13(X49,X50,set_intersection2(X51,X52)),X51)
| sP2(X49,X50,set_intersection2(X51,X52))
| apply(sK5,sK13(X49,X50,set_intersection2(X51,X52))) = apply(relation_dom_restriction(sK5,X49),sK13(X49,X50,set_intersection2(X51,X52))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_638])]) ).
fof(f2516,plain,
( ! [X50,X51,X49,X52] :
( in(sK13(X49,X50,set_intersection2(X51,X52)),X51)
| sP2(X49,X50,set_intersection2(X51,X52))
| apply(sK5,sK13(X49,X50,set_intersection2(X51,X52))) = apply(relation_dom_restriction(sK5,X49),sK13(X49,X50,set_intersection2(X51,X52))) )
| ~ spl22_229
| ~ spl22_238 ),
inference(resolution,[],[f2440,f2272]) ).
fof(f9253,plain,
( spl22_637
| spl22_81
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f6955,f6919,f730,f9250]) ).
fof(f9250,plain,
( spl22_637
<=> apply(relation_dom_restriction(sK5,sK5),sK10(sK5)) = apply(sK5,sK10(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_637])]) ).
fof(f6955,plain,
( apply(relation_dom_restriction(sK5,sK5),sK10(sK5)) = apply(sK5,sK10(sK5))
| spl22_81
| ~ spl22_498 ),
inference(resolution,[],[f6920,f732]) ).
fof(f9248,plain,
( spl22_636
| ~ spl22_226
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2515,f2439,f2237,f9246]) ).
fof(f9246,plain,
( spl22_636
<=> ! [X48,X47,X46,X45] :
( in(sK13(X45,X46,set_intersection2(X47,X48)),X47)
| sP2(X45,X46,set_intersection2(X47,X48))
| apply(sK5,sK13(X45,X46,set_intersection2(X47,X48))) = apply(relation_dom_restriction(sK5,X46),sK13(X45,X46,set_intersection2(X47,X48))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_636])]) ).
fof(f2515,plain,
( ! [X48,X46,X47,X45] :
( in(sK13(X45,X46,set_intersection2(X47,X48)),X47)
| sP2(X45,X46,set_intersection2(X47,X48))
| apply(sK5,sK13(X45,X46,set_intersection2(X47,X48))) = apply(relation_dom_restriction(sK5,X46),sK13(X45,X46,set_intersection2(X47,X48))) )
| ~ spl22_226
| ~ spl22_238 ),
inference(resolution,[],[f2440,f2238]) ).
fof(f9244,plain,
( spl22_635
| ~ spl22_228
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2490,f2435,f2256,f9242]) ).
fof(f9242,plain,
( spl22_635
<=> ! [X69,X71,X70,X72] :
( in(sK13(set_intersection2(X69,X70),X71,X72),X70)
| sP2(set_intersection2(X69,X70),X71,X72)
| apply(relation_dom_restriction(sK5,X72),sK13(set_intersection2(X69,X70),X71,X72)) = apply(sK5,sK13(set_intersection2(X69,X70),X71,X72)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_635])]) ).
fof(f2490,plain,
( ! [X72,X70,X71,X69] :
( in(sK13(set_intersection2(X69,X70),X71,X72),X70)
| sP2(set_intersection2(X69,X70),X71,X72)
| apply(relation_dom_restriction(sK5,X72),sK13(set_intersection2(X69,X70),X71,X72)) = apply(sK5,sK13(set_intersection2(X69,X70),X71,X72)) )
| ~ spl22_228
| ~ spl22_237 ),
inference(resolution,[],[f2436,f2257]) ).
fof(f9240,plain,
( spl22_634
| ~ spl22_225
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2486,f2435,f2222,f9238]) ).
fof(f9238,plain,
( spl22_634
<=> ! [X55,X54,X53,X56] :
( in(sK13(X53,set_intersection2(X54,X55),X56),X55)
| sP2(X53,set_intersection2(X54,X55),X56)
| apply(relation_dom_restriction(sK5,X56),sK13(X53,set_intersection2(X54,X55),X56)) = apply(sK5,sK13(X53,set_intersection2(X54,X55),X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_634])]) ).
fof(f2486,plain,
( ! [X56,X54,X55,X53] :
( in(sK13(X53,set_intersection2(X54,X55),X56),X55)
| sP2(X53,set_intersection2(X54,X55),X56)
| apply(relation_dom_restriction(sK5,X56),sK13(X53,set_intersection2(X54,X55),X56)) = apply(sK5,sK13(X53,set_intersection2(X54,X55),X56)) )
| ~ spl22_225
| ~ spl22_237 ),
inference(resolution,[],[f2436,f2223]) ).
fof(f9236,plain,
( spl22_633
| ~ spl22_229
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2485,f2435,f2271,f9234]) ).
fof(f9234,plain,
( spl22_633
<=> ! [X51,X50,X49,X52] :
( in(sK13(X49,X50,set_intersection2(X51,X52)),X52)
| sP2(X49,X50,set_intersection2(X51,X52))
| apply(sK5,sK13(X49,X50,set_intersection2(X51,X52))) = apply(relation_dom_restriction(sK5,X49),sK13(X49,X50,set_intersection2(X51,X52))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_633])]) ).
fof(f2485,plain,
( ! [X50,X51,X49,X52] :
( in(sK13(X49,X50,set_intersection2(X51,X52)),X52)
| sP2(X49,X50,set_intersection2(X51,X52))
| apply(sK5,sK13(X49,X50,set_intersection2(X51,X52))) = apply(relation_dom_restriction(sK5,X49),sK13(X49,X50,set_intersection2(X51,X52))) )
| ~ spl22_229
| ~ spl22_237 ),
inference(resolution,[],[f2436,f2272]) ).
fof(f9232,plain,
( spl22_632
| ~ spl22_226
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2484,f2435,f2237,f9230]) ).
fof(f9230,plain,
( spl22_632
<=> ! [X48,X47,X46,X45] :
( in(sK13(X45,X46,set_intersection2(X47,X48)),X48)
| sP2(X45,X46,set_intersection2(X47,X48))
| apply(sK5,sK13(X45,X46,set_intersection2(X47,X48))) = apply(relation_dom_restriction(sK5,X46),sK13(X45,X46,set_intersection2(X47,X48))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_632])]) ).
fof(f2484,plain,
( ! [X48,X46,X47,X45] :
( in(sK13(X45,X46,set_intersection2(X47,X48)),X48)
| sP2(X45,X46,set_intersection2(X47,X48))
| apply(sK5,sK13(X45,X46,set_intersection2(X47,X48))) = apply(relation_dom_restriction(sK5,X46),sK13(X45,X46,set_intersection2(X47,X48))) )
| ~ spl22_226
| ~ spl22_237 ),
inference(resolution,[],[f2436,f2238]) ).
fof(f9228,plain,
( spl22_631
| ~ spl22_137
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2281,f2271,f1213,f9226]) ).
fof(f9226,plain,
( spl22_631
<=> ! [X25,X24,X23] :
( sP2(X23,X24,sK10(powerset(X25)))
| apply(sK5,sK13(X23,X24,sK10(powerset(X25)))) = apply(relation_dom_restriction(sK5,X23),sK13(X23,X24,sK10(powerset(X25))))
| element(sK13(X23,X24,sK10(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_631])]) ).
fof(f2281,plain,
( ! [X24,X25,X23] :
( sP2(X23,X24,sK10(powerset(X25)))
| apply(sK5,sK13(X23,X24,sK10(powerset(X25)))) = apply(relation_dom_restriction(sK5,X23),sK13(X23,X24,sK10(powerset(X25))))
| element(sK13(X23,X24,sK10(powerset(X25))),X25) )
| ~ spl22_137
| ~ spl22_229 ),
inference(resolution,[],[f2272,f1214]) ).
fof(f9224,plain,
( spl22_630
| ~ spl22_137
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2266,f2256,f1213,f9222]) ).
fof(f9222,plain,
( spl22_630
<=> ! [X22,X24,X23] :
( sP2(sK10(powerset(X22)),X23,X24)
| apply(relation_dom_restriction(sK5,X24),sK13(sK10(powerset(X22)),X23,X24)) = apply(sK5,sK13(sK10(powerset(X22)),X23,X24))
| element(sK13(sK10(powerset(X22)),X23,X24),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_630])]) ).
fof(f2266,plain,
( ! [X24,X22,X23] :
( sP2(sK10(powerset(X22)),X23,X24)
| apply(relation_dom_restriction(sK5,X24),sK13(sK10(powerset(X22)),X23,X24)) = apply(sK5,sK13(sK10(powerset(X22)),X23,X24))
| element(sK13(sK10(powerset(X22)),X23,X24),X22) )
| ~ spl22_137
| ~ spl22_228 ),
inference(resolution,[],[f2257,f1214]) ).
fof(f9220,plain,
( spl22_629
| ~ spl22_137
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2247,f2237,f1213,f9218]) ).
fof(f9218,plain,
( spl22_629
<=> ! [X25,X24,X23] :
( sP2(X23,X24,sK10(powerset(X25)))
| apply(sK5,sK13(X23,X24,sK10(powerset(X25)))) = apply(relation_dom_restriction(sK5,X24),sK13(X23,X24,sK10(powerset(X25))))
| element(sK13(X23,X24,sK10(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_629])]) ).
fof(f2247,plain,
( ! [X24,X25,X23] :
( sP2(X23,X24,sK10(powerset(X25)))
| apply(sK5,sK13(X23,X24,sK10(powerset(X25)))) = apply(relation_dom_restriction(sK5,X24),sK13(X23,X24,sK10(powerset(X25))))
| element(sK13(X23,X24,sK10(powerset(X25))),X25) )
| ~ spl22_137
| ~ spl22_226 ),
inference(resolution,[],[f2238,f1214]) ).
fof(f9216,plain,
( spl22_628
| ~ spl22_137
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2232,f2222,f1213,f9214]) ).
fof(f9214,plain,
( spl22_628
<=> ! [X22,X24,X23] :
( sP2(X22,sK10(powerset(X23)),X24)
| apply(relation_dom_restriction(sK5,X24),sK13(X22,sK10(powerset(X23)),X24)) = apply(sK5,sK13(X22,sK10(powerset(X23)),X24))
| element(sK13(X22,sK10(powerset(X23)),X24),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_628])]) ).
fof(f2232,plain,
( ! [X24,X22,X23] :
( sP2(X22,sK10(powerset(X23)),X24)
| apply(relation_dom_restriction(sK5,X24),sK13(X22,sK10(powerset(X23)),X24)) = apply(sK5,sK13(X22,sK10(powerset(X23)),X24))
| element(sK13(X22,sK10(powerset(X23)),X24),X23) )
| ~ spl22_137
| ~ spl22_225 ),
inference(resolution,[],[f2223,f1214]) ).
fof(f9207,plain,
( spl22_627
| spl22_47
| ~ spl22_498 ),
inference(avatar_split_clause,[],[f6954,f6919,f475,f9204]) ).
fof(f9204,plain,
( spl22_627
<=> apply(relation_dom_restriction(sK5,sK3),sK10(sK3)) = apply(sK5,sK10(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_627])]) ).
fof(f6954,plain,
( apply(relation_dom_restriction(sK5,sK3),sK10(sK3)) = apply(sK5,sK10(sK3))
| spl22_47
| ~ spl22_498 ),
inference(resolution,[],[f6920,f477]) ).
fof(f8839,plain,
( spl22_626
| ~ spl22_20
| ~ spl22_19
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2946,f2799,f309,f314,f8836]) ).
fof(f8836,plain,
( spl22_626
<=> sK20 = relation_dom_restriction(sK20,relation_dom(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_626])]) ).
fof(f2946,plain,
( ~ function(sK20)
| sK20 = relation_dom_restriction(sK20,relation_dom(sK20))
| ~ spl22_19
| ~ spl22_276 ),
inference(resolution,[],[f2800,f311]) ).
fof(f8791,plain,
( spl22_625
| ~ spl22_18
| ~ spl22_17
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2945,f2799,f299,f304,f8788]) ).
fof(f8788,plain,
( spl22_625
<=> sK19 = relation_dom_restriction(sK19,relation_dom(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_625])]) ).
fof(f2945,plain,
( ~ function(sK19)
| sK19 = relation_dom_restriction(sK19,relation_dom(sK19))
| ~ spl22_17
| ~ spl22_276 ),
inference(resolution,[],[f2800,f301]) ).
fof(f8786,plain,
( spl22_624
| ~ spl22_131
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2864,f2711,f1173,f8784]) ).
fof(f8784,plain,
( spl22_624
<=> ! [X29,X30] :
( sP2(sK15,X29,sK10(powerset(X30)))
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_624])]) ).
fof(f2864,plain,
( ! [X29,X30] :
( sP2(sK15,X29,sK10(powerset(X30)))
| ~ empty(X30) )
| ~ spl22_131
| ~ spl22_255 ),
inference(resolution,[],[f2712,f1174]) ).
fof(f8782,plain,
( spl22_623
| ~ spl22_236
| ~ spl22_255 ),
inference(avatar_split_clause,[],[f2861,f2711,f2331,f8780]) ).
fof(f8780,plain,
( spl22_623
<=> ! [X24,X23] :
( sP2(sK15,X23,relation_dom(X24))
| ~ sP0(X24,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_623])]) ).
fof(f2861,plain,
( ! [X24,X23] :
( sP2(sK15,X23,relation_dom(X24))
| ~ sP0(X24,sK15) )
| ~ spl22_236
| ~ spl22_255 ),
inference(resolution,[],[f2712,f2332]) ).
fof(f8778,plain,
( spl22_622
| ~ spl22_131
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2849,f2707,f1173,f8776]) ).
fof(f8776,plain,
( spl22_622
<=> ! [X29,X30] :
( sP2(X29,sK15,sK10(powerset(X30)))
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_622])]) ).
fof(f2849,plain,
( ! [X29,X30] :
( sP2(X29,sK15,sK10(powerset(X30)))
| ~ empty(X30) )
| ~ spl22_131
| ~ spl22_254 ),
inference(resolution,[],[f2708,f1174]) ).
fof(f8774,plain,
( spl22_621
| ~ spl22_236
| ~ spl22_254 ),
inference(avatar_split_clause,[],[f2846,f2707,f2331,f8772]) ).
fof(f8772,plain,
( spl22_621
<=> ! [X24,X23] :
( sP2(X23,sK15,relation_dom(X24))
| ~ sP0(X24,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_621])]) ).
fof(f2846,plain,
( ! [X24,X23] :
( sP2(X23,sK15,relation_dom(X24))
| ~ sP0(X24,sK15) )
| ~ spl22_236
| ~ spl22_254 ),
inference(resolution,[],[f2708,f2332]) ).
fof(f8770,plain,
( spl22_620
| ~ spl22_131
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2829,f2703,f1173,f8768]) ).
fof(f8768,plain,
( spl22_620
<=> ! [X29,X28] :
( sP2(X28,sK10(powerset(X29)),sK15)
| ~ empty(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_620])]) ).
fof(f2829,plain,
( ! [X28,X29] :
( sP2(X28,sK10(powerset(X29)),sK15)
| ~ empty(X29) )
| ~ spl22_131
| ~ spl22_253 ),
inference(resolution,[],[f2704,f1174]) ).
fof(f8766,plain,
( spl22_619
| ~ spl22_236
| ~ spl22_253 ),
inference(avatar_split_clause,[],[f2826,f2703,f2331,f8764]) ).
fof(f8764,plain,
( spl22_619
<=> ! [X22,X23] :
( sP2(X22,relation_dom(X23),sK15)
| ~ sP0(X23,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_619])]) ).
fof(f2826,plain,
( ! [X22,X23] :
( sP2(X22,relation_dom(X23),sK15)
| ~ sP0(X23,sK15) )
| ~ spl22_236
| ~ spl22_253 ),
inference(resolution,[],[f2704,f2332]) ).
fof(f8762,plain,
( spl22_618
| ~ spl22_131
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2814,f2699,f1173,f8760]) ).
fof(f8760,plain,
( spl22_618
<=> ! [X29,X28] :
( sP2(sK10(powerset(X28)),X29,sK15)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_618])]) ).
fof(f2814,plain,
( ! [X28,X29] :
( sP2(sK10(powerset(X28)),X29,sK15)
| ~ empty(X28) )
| ~ spl22_131
| ~ spl22_252 ),
inference(resolution,[],[f2700,f1174]) ).
fof(f8745,plain,
( spl22_617
| ~ spl22_236
| ~ spl22_252 ),
inference(avatar_split_clause,[],[f2811,f2699,f2331,f8743]) ).
fof(f8743,plain,
( spl22_617
<=> ! [X22,X23] :
( sP2(relation_dom(X22),X23,sK15)
| ~ sP0(X22,sK15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_617])]) ).
fof(f2811,plain,
( ! [X22,X23] :
( sP2(relation_dom(X22),X23,sK15)
| ~ sP0(X22,sK15) )
| ~ spl22_236
| ~ spl22_252 ),
inference(resolution,[],[f2700,f2332]) ).
fof(f8741,plain,
( spl22_616
| ~ spl22_124
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2678,f2571,f1103,f8739]) ).
fof(f8739,plain,
( spl22_616
<=> ! [X32,X33] :
( ~ sP0(X32,X33)
| ~ empty(X33)
| empty(relation_dom(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_616])]) ).
fof(f2678,plain,
( ! [X32,X33] :
( ~ sP0(X32,X33)
| ~ empty(X33)
| empty(relation_dom(X32)) )
| ~ spl22_124
| ~ spl22_250 ),
inference(resolution,[],[f2572,f1104]) ).
fof(f8737,plain,
( spl22_615
| ~ spl22_150
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2412,f2331,f1366,f8735]) ).
fof(f2412,plain,
( ! [X18,X17] :
( ~ sP0(X17,sK15)
| sP0(X17,X18)
| ~ empty(X18) )
| ~ spl22_150
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1367]) ).
fof(f8733,plain,
( spl22_614
| ~ spl22_36
| ~ spl22_235 ),
inference(avatar_split_clause,[],[f2387,f2327,f393,f8731]) ).
fof(f8731,plain,
( spl22_614
<=> ! [X1] :
( sK15 = relation_dom(relation_dom(relation_dom(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_614])]) ).
fof(f2387,plain,
( ! [X1] :
( sK15 = relation_dom(relation_dom(relation_dom(X1)))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_235 ),
inference(resolution,[],[f2328,f394]) ).
fof(f8729,plain,
( spl22_613
| ~ spl22_34
| ~ spl22_235 ),
inference(avatar_split_clause,[],[f2386,f2327,f385,f8727]) ).
fof(f8727,plain,
( spl22_613
<=> ! [X0] :
( sK15 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_613])]) ).
fof(f2386,plain,
( ! [X0] :
( sK15 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_235 ),
inference(resolution,[],[f2328,f386]) ).
fof(f8725,plain,
( spl22_612
| ~ spl22_36
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f2370,f2306,f393,f8723]) ).
fof(f8723,plain,
( spl22_612
<=> ! [X1] :
( sK15 = relation_dom(relation_rng(relation_dom(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_612])]) ).
fof(f2370,plain,
( ! [X1] :
( sK15 = relation_dom(relation_rng(relation_dom(X1)))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_234 ),
inference(resolution,[],[f2307,f394]) ).
fof(f8721,plain,
( spl22_611
| ~ spl22_34
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f2369,f2306,f385,f8719]) ).
fof(f8719,plain,
( spl22_611
<=> ! [X0] :
( sK15 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_611])]) ).
fof(f2369,plain,
( ! [X0] :
( sK15 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_234 ),
inference(resolution,[],[f2307,f386]) ).
fof(f8717,plain,
( spl22_610
| ~ spl22_36
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2353,f2302,f393,f8715]) ).
fof(f8715,plain,
( spl22_610
<=> ! [X1] :
( sK15 = relation_rng(relation_dom(relation_dom(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_610])]) ).
fof(f2353,plain,
( ! [X1] :
( sK15 = relation_rng(relation_dom(relation_dom(X1)))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_233 ),
inference(resolution,[],[f2303,f394]) ).
fof(f8713,plain,
( spl22_609
| ~ spl22_34
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f2352,f2302,f385,f8711]) ).
fof(f8711,plain,
( spl22_609
<=> ! [X0] :
( sK15 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_609])]) ).
fof(f2352,plain,
( ! [X0] :
( sK15 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_233 ),
inference(resolution,[],[f2303,f386]) ).
fof(f8709,plain,
( spl22_608
| ~ spl22_36
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2336,f2298,f393,f8707]) ).
fof(f8707,plain,
( spl22_608
<=> ! [X1] :
( sK15 = relation_rng(relation_rng(relation_dom(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_608])]) ).
fof(f2336,plain,
( ! [X1] :
( sK15 = relation_rng(relation_rng(relation_dom(X1)))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_232 ),
inference(resolution,[],[f2299,f394]) ).
fof(f8691,plain,
( spl22_607
| ~ spl22_34
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f2335,f2298,f385,f8689]) ).
fof(f8689,plain,
( spl22_607
<=> ! [X0] :
( sK15 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_607])]) ).
fof(f2335,plain,
( ! [X0] :
( sK15 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_232 ),
inference(resolution,[],[f2299,f386]) ).
fof(f8687,plain,
( spl22_606
| ~ spl22_119
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2184,f2120,f1078,f8685]) ).
fof(f8685,plain,
( spl22_606
<=> ! [X6] :
( ~ empty(X6)
| sK15 = relation_dom(sK10(powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_606])]) ).
fof(f2184,plain,
( ! [X6] :
( ~ empty(X6)
| sK15 = relation_dom(sK10(powerset(X6))) )
| ~ spl22_119
| ~ spl22_216 ),
inference(resolution,[],[f2121,f1079]) ).
fof(f8683,plain,
( spl22_605
| ~ spl22_118
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2183,f2120,f1074,f8681]) ).
fof(f8681,plain,
( spl22_605
<=> ! [X5] :
( ~ empty(X5)
| sK15 = relation_rng(sK10(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_605])]) ).
fof(f2183,plain,
( ! [X5] :
( ~ empty(X5)
| sK15 = relation_rng(sK10(powerset(X5))) )
| ~ spl22_118
| ~ spl22_216 ),
inference(resolution,[],[f2121,f1075]) ).
fof(f8678,plain,
( ~ spl22_108
| spl22_604
| ~ spl22_61
| ~ spl22_196 ),
inference(avatar_split_clause,[],[f1949,f1921,f594,f8676,f925]) ).
fof(f925,plain,
( spl22_108
<=> sP1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_108])]) ).
fof(f8676,plain,
( spl22_604
<=> ! [X0] :
( sK15 != X0
| sP0(sK15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_604])]) ).
fof(f594,plain,
( spl22_61
<=> ! [X0,X1] :
( sP0(X0,X1)
| relation_rng(X0) != X1
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_61])]) ).
fof(f1921,plain,
( spl22_196
<=> sK15 = relation_rng(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_196])]) ).
fof(f1949,plain,
( ! [X0] :
( sK15 != X0
| sP0(sK15,X0)
| ~ sP1(sK15) )
| ~ spl22_61
| ~ spl22_196 ),
inference(superposition,[],[f595,f1923]) ).
fof(f1923,plain,
( sK15 = relation_rng(sK15)
| ~ spl22_196 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f595,plain,
( ! [X0,X1] :
( relation_rng(X0) != X1
| sP0(X0,X1)
| ~ sP1(X0) )
| ~ spl22_61 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f8585,plain,
( spl22_603
| ~ spl22_72
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2289,f2286,f660,f8583]) ).
fof(f8583,plain,
( spl22_603
<=> ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(X2,X1)
| apply(X0,sK9(X0,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_603])]) ).
fof(f660,plain,
( spl22_72
<=> ! [X5,X0,X1] :
( apply(X0,sK9(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_72])]) ).
fof(f2289,plain,
( ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| apply(relation_dom_restriction(sK5,X1),sK7(X0,X1)) = apply(sK5,sK7(X0,X1))
| ~ in(X2,X1)
| apply(X0,sK9(X0,X2)) = X2 )
| ~ spl22_72
| ~ spl22_230 ),
inference(resolution,[],[f2287,f661]) ).
fof(f661,plain,
( ! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ in(X5,X1)
| apply(X0,sK9(X0,X5)) = X5 )
| ~ spl22_72 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f8247,plain,
( spl22_602
| ~ spl22_71
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2290,f2286,f656,f8245]) ).
fof(f8245,plain,
( spl22_602
<=> ! [X4,X5,X3] :
( sK7(X3,X4) = apply(X3,sK8(X3,X4))
| apply(relation_dom_restriction(sK5,X4),sK7(X3,X4)) = apply(sK5,sK7(X3,X4))
| ~ in(X5,X4)
| in(sK9(X3,X5),relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_602])]) ).
fof(f656,plain,
( spl22_71
<=> ! [X5,X0,X1] :
( in(sK9(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_71])]) ).
fof(f2290,plain,
( ! [X3,X4,X5] :
( sK7(X3,X4) = apply(X3,sK8(X3,X4))
| apply(relation_dom_restriction(sK5,X4),sK7(X3,X4)) = apply(sK5,sK7(X3,X4))
| ~ in(X5,X4)
| in(sK9(X3,X5),relation_dom(X3)) )
| ~ spl22_71
| ~ spl22_230 ),
inference(resolution,[],[f2287,f657]) ).
fof(f657,plain,
( ! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ in(X5,X1)
| in(sK9(X0,X5),relation_dom(X0)) )
| ~ spl22_71 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f8243,plain,
( spl22_601
| ~ spl22_83
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2284,f2271,f740,f8241]) ).
fof(f8241,plain,
( spl22_601
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_601])]) ).
fof(f740,plain,
( spl22_83
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_83])]) ).
fof(f2284,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) )
| ~ spl22_83
| ~ spl22_229 ),
inference(duplicate_literal_removal,[],[f2274]) ).
fof(f2274,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X0),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_83
| ~ spl22_229 ),
inference(resolution,[],[f2272,f741]) ).
fof(f741,plain,
( ! [X2,X0,X1] :
( ~ in(sK13(X0,X1,X2),X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_83 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f8239,plain,
( spl22_600
| ~ spl22_141
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2280,f2271,f1277,f8237]) ).
fof(f8237,plain,
( spl22_600
<=> ! [X22,X20,X21] :
( sP2(X20,X21,sK6(X22))
| apply(sK5,sK13(X20,X21,sK6(X22))) = apply(relation_dom_restriction(sK5,X20),sK13(X20,X21,sK6(X22)))
| element(sK13(X20,X21,sK6(X22)),X22)
| empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_600])]) ).
fof(f2280,plain,
( ! [X21,X22,X20] :
( sP2(X20,X21,sK6(X22))
| apply(sK5,sK13(X20,X21,sK6(X22))) = apply(relation_dom_restriction(sK5,X20),sK13(X20,X21,sK6(X22)))
| element(sK13(X20,X21,sK6(X22)),X22)
| empty(X22) )
| ~ spl22_141
| ~ spl22_229 ),
inference(resolution,[],[f2272,f1278]) ).
fof(f8235,plain,
( spl22_599
| ~ spl22_141
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2265,f2256,f1277,f8233]) ).
fof(f8233,plain,
( spl22_599
<=> ! [X20,X21,X19] :
( sP2(sK6(X19),X20,X21)
| apply(relation_dom_restriction(sK5,X21),sK13(sK6(X19),X20,X21)) = apply(sK5,sK13(sK6(X19),X20,X21))
| element(sK13(sK6(X19),X20,X21),X19)
| empty(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_599])]) ).
fof(f2265,plain,
( ! [X21,X19,X20] :
( sP2(sK6(X19),X20,X21)
| apply(relation_dom_restriction(sK5,X21),sK13(sK6(X19),X20,X21)) = apply(sK5,sK13(sK6(X19),X20,X21))
| element(sK13(sK6(X19),X20,X21),X19)
| empty(X19) )
| ~ spl22_141
| ~ spl22_228 ),
inference(resolution,[],[f2257,f1278]) ).
fof(f8231,plain,
( spl22_598
| ~ spl22_83
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2250,f2237,f740,f8229]) ).
fof(f8229,plain,
( spl22_598
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_598])]) ).
fof(f2250,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1) )
| ~ spl22_83
| ~ spl22_226 ),
inference(duplicate_literal_removal,[],[f2240]) ).
fof(f2240,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| apply(sK5,sK13(X0,X1,X2)) = apply(relation_dom_restriction(sK5,X1),sK13(X0,X1,X2))
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2) )
| ~ spl22_83
| ~ spl22_226 ),
inference(resolution,[],[f2238,f741]) ).
fof(f8227,plain,
( spl22_597
| ~ spl22_141
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2246,f2237,f1277,f8225]) ).
fof(f8225,plain,
( spl22_597
<=> ! [X22,X20,X21] :
( sP2(X20,X21,sK6(X22))
| apply(sK5,sK13(X20,X21,sK6(X22))) = apply(relation_dom_restriction(sK5,X21),sK13(X20,X21,sK6(X22)))
| element(sK13(X20,X21,sK6(X22)),X22)
| empty(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_597])]) ).
fof(f2246,plain,
( ! [X21,X22,X20] :
( sP2(X20,X21,sK6(X22))
| apply(sK5,sK13(X20,X21,sK6(X22))) = apply(relation_dom_restriction(sK5,X21),sK13(X20,X21,sK6(X22)))
| element(sK13(X20,X21,sK6(X22)),X22)
| empty(X22) )
| ~ spl22_141
| ~ spl22_226 ),
inference(resolution,[],[f2238,f1278]) ).
fof(f8222,plain,
( spl22_596
| ~ spl22_141
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2231,f2222,f1277,f8220]) ).
fof(f8220,plain,
( spl22_596
<=> ! [X20,X21,X19] :
( sP2(X19,sK6(X20),X21)
| apply(relation_dom_restriction(sK5,X21),sK13(X19,sK6(X20),X21)) = apply(sK5,sK13(X19,sK6(X20),X21))
| element(sK13(X19,sK6(X20),X21),X20)
| empty(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_596])]) ).
fof(f2231,plain,
( ! [X21,X19,X20] :
( sP2(X19,sK6(X20),X21)
| apply(relation_dom_restriction(sK5,X21),sK13(X19,sK6(X20),X21)) = apply(sK5,sK13(X19,sK6(X20),X21))
| element(sK13(X19,sK6(X20),X21),X20)
| empty(X20) )
| ~ spl22_141
| ~ spl22_225 ),
inference(resolution,[],[f2223,f1278]) ).
fof(f8135,plain,
( spl22_595
| ~ spl22_212
| ~ spl22_238 ),
inference(avatar_split_clause,[],[f2503,f2439,f2089,f8133]) ).
fof(f8133,plain,
( spl22_595
<=> ! [X6,X4,X5] :
( in(sK7(X4,set_intersection2(X5,X6)),X5)
| sP0(X4,set_intersection2(X5,X6))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,set_intersection2(X5,X6))) = apply(sK5,sK8(X4,set_intersection2(X5,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_595])]) ).
fof(f2503,plain,
( ! [X6,X4,X5] :
( in(sK7(X4,set_intersection2(X5,X6)),X5)
| sP0(X4,set_intersection2(X5,X6))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,set_intersection2(X5,X6))) = apply(sK5,sK8(X4,set_intersection2(X5,X6))) )
| ~ spl22_212
| ~ spl22_238 ),
inference(resolution,[],[f2440,f2090]) ).
fof(f8131,plain,
( spl22_594
| ~ spl22_212
| ~ spl22_237 ),
inference(avatar_split_clause,[],[f2472,f2435,f2089,f8129]) ).
fof(f8129,plain,
( spl22_594
<=> ! [X6,X4,X5] :
( in(sK7(X4,set_intersection2(X5,X6)),X6)
| sP0(X4,set_intersection2(X5,X6))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,set_intersection2(X5,X6))) = apply(sK5,sK8(X4,set_intersection2(X5,X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_594])]) ).
fof(f2472,plain,
( ! [X6,X4,X5] :
( in(sK7(X4,set_intersection2(X5,X6)),X6)
| sP0(X4,set_intersection2(X5,X6))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,set_intersection2(X5,X6))) = apply(sK5,sK8(X4,set_intersection2(X5,X6))) )
| ~ spl22_212
| ~ spl22_237 ),
inference(resolution,[],[f2436,f2090]) ).
fof(f8127,plain,
( spl22_593
| ~ spl22_137
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2098,f2089,f1213,f8125]) ).
fof(f8125,plain,
( spl22_593
<=> ! [X14,X15] :
( sP0(X14,sK10(powerset(X15)))
| apply(relation_dom_restriction(sK5,relation_dom(X14)),sK8(X14,sK10(powerset(X15)))) = apply(sK5,sK8(X14,sK10(powerset(X15))))
| element(sK7(X14,sK10(powerset(X15))),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_593])]) ).
fof(f2098,plain,
( ! [X14,X15] :
( sP0(X14,sK10(powerset(X15)))
| apply(relation_dom_restriction(sK5,relation_dom(X14)),sK8(X14,sK10(powerset(X15)))) = apply(sK5,sK8(X14,sK10(powerset(X15))))
| element(sK7(X14,sK10(powerset(X15))),X15) )
| ~ spl22_137
| ~ spl22_212 ),
inference(resolution,[],[f2090,f1214]) ).
fof(f8056,plain,
( spl22_591
| ~ spl22_592
| ~ spl22_214
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7098,f7070,f2112,f8053,f8049]) ).
fof(f8053,plain,
( spl22_592
<=> sP0(sK5,sK10(apply(sK5,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_592])]) ).
fof(f7098,plain,
( ~ sP0(sK5,sK10(apply(sK5,sK4)))
| empty(apply(sK5,sK4))
| ~ spl22_214
| ~ spl22_513 ),
inference(resolution,[],[f7071,f2113]) ).
fof(f7962,plain,
( ~ spl22_42
| spl22_590
| ~ spl22_7
| ~ spl22_94
| ~ spl22_197
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2950,f2799,f1926,f812,f249,f7959,f433]) ).
fof(f7959,plain,
( spl22_590
<=> sK15 = relation_dom_restriction(sK15,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_590])]) ).
fof(f2950,plain,
( sK15 = relation_dom_restriction(sK15,sK15)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_94
| ~ spl22_197
| ~ spl22_276 ),
inference(forward_demodulation,[],[f2949,f1928]) ).
fof(f2949,plain,
( sK15 = relation_dom_restriction(sK15,relation_dom(sK15))
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_94
| ~ spl22_276 ),
inference(forward_demodulation,[],[f2948,f814]) ).
fof(f2948,plain,
( ~ function(sK15)
| empty_set = relation_dom_restriction(empty_set,relation_dom(empty_set))
| ~ spl22_7
| ~ spl22_94
| ~ spl22_276 ),
inference(forward_demodulation,[],[f2939,f814]) ).
fof(f2939,plain,
( ~ function(empty_set)
| empty_set = relation_dom_restriction(empty_set,relation_dom(empty_set))
| ~ spl22_7
| ~ spl22_276 ),
inference(resolution,[],[f2800,f251]) ).
fof(f7957,plain,
( spl22_589
| ~ spl22_36
| ~ spl22_243 ),
inference(avatar_split_clause,[],[f2544,f2460,f393,f7955]) ).
fof(f7955,plain,
( spl22_589
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_589])]) ).
fof(f2460,plain,
( spl22_243
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_243])]) ).
fof(f2544,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_243 ),
inference(resolution,[],[f2461,f394]) ).
fof(f2461,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(X0,X1)
| ~ empty(X1) )
| ~ spl22_243 ),
inference(avatar_component_clause,[],[f2460]) ).
fof(f7953,plain,
( spl22_588
| ~ spl22_64
| ~ spl22_223 ),
inference(avatar_split_clause,[],[f2220,f2164,f606,f7951]) ).
fof(f7951,plain,
( spl22_588
<=> ! [X9,X8] :
( ~ empty(X8)
| sK15 = set_intersection2(X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_588])]) ).
fof(f2164,plain,
( spl22_223
<=> ! [X25,X26] :
( sP2(X25,X26,sK15)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_223])]) ).
fof(f2220,plain,
( ! [X8,X9] :
( ~ empty(X8)
| sK15 = set_intersection2(X9,X8) )
| ~ spl22_64
| ~ spl22_223 ),
inference(resolution,[],[f2165,f607]) ).
fof(f2165,plain,
( ! [X26,X25] :
( sP2(X25,X26,sK15)
| ~ empty(X25) )
| ~ spl22_223 ),
inference(avatar_component_clause,[],[f2164]) ).
fof(f7949,plain,
( spl22_587
| ~ spl22_64
| ~ spl22_221 ),
inference(avatar_split_clause,[],[f2211,f2156,f606,f7947]) ).
fof(f7947,plain,
( spl22_587
<=> ! [X9,X8] :
( ~ empty(X8)
| sK15 = set_intersection2(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_587])]) ).
fof(f2156,plain,
( spl22_221
<=> ! [X25,X26] :
( sP2(X25,X26,sK15)
| ~ empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_221])]) ).
fof(f2211,plain,
( ! [X8,X9] :
( ~ empty(X8)
| sK15 = set_intersection2(X8,X9) )
| ~ spl22_64
| ~ spl22_221 ),
inference(resolution,[],[f2157,f607]) ).
fof(f2157,plain,
( ! [X26,X25] :
( sP2(X25,X26,sK15)
| ~ empty(X26) )
| ~ spl22_221 ),
inference(avatar_component_clause,[],[f2156]) ).
fof(f7945,plain,
( spl22_586
| ~ spl22_64
| ~ spl22_218 ),
inference(avatar_split_clause,[],[f2200,f2144,f606,f7943]) ).
fof(f7943,plain,
( spl22_586
<=> ! [X9,X8] :
( ~ empty(X8)
| set_intersection2(X9,X8) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_586])]) ).
fof(f2144,plain,
( spl22_218
<=> ! [X2,X3] :
( sP2(X2,X3,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_218])]) ).
fof(f2200,plain,
( ! [X8,X9] :
( ~ empty(X8)
| set_intersection2(X9,X8) = X8 )
| ~ spl22_64
| ~ spl22_218 ),
inference(resolution,[],[f2145,f607]) ).
fof(f2145,plain,
( ! [X2,X3] :
( sP2(X2,X3,X2)
| ~ empty(X2) )
| ~ spl22_218 ),
inference(avatar_component_clause,[],[f2144]) ).
fof(f7941,plain,
( spl22_585
| ~ spl22_64
| ~ spl22_217 ),
inference(avatar_split_clause,[],[f2192,f2124,f606,f7939]) ).
fof(f7939,plain,
( spl22_585
<=> ! [X9,X8] :
( ~ empty(X8)
| set_intersection2(X8,X9) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_585])]) ).
fof(f2124,plain,
( spl22_217
<=> ! [X2,X3] :
( sP2(X2,X3,X3)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_217])]) ).
fof(f2192,plain,
( ! [X8,X9] :
( ~ empty(X8)
| set_intersection2(X8,X9) = X8 )
| ~ spl22_64
| ~ spl22_217 ),
inference(resolution,[],[f2125,f607]) ).
fof(f2125,plain,
( ! [X2,X3] :
( sP2(X2,X3,X3)
| ~ empty(X3) )
| ~ spl22_217 ),
inference(avatar_component_clause,[],[f2124]) ).
fof(f7937,plain,
( spl22_584
| ~ spl22_137
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7096,f7070,f1213,f7935]) ).
fof(f7935,plain,
( spl22_584
<=> ! [X33] :
( ~ sP0(sK5,sK10(powerset(X33)))
| element(apply(sK5,sK4),X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_584])]) ).
fof(f7096,plain,
( ! [X33] :
( ~ sP0(sK5,sK10(powerset(X33)))
| element(apply(sK5,sK4),X33) )
| ~ spl22_137
| ~ spl22_513 ),
inference(resolution,[],[f7071,f1214]) ).
fof(f7933,plain,
( spl22_583
| ~ spl22_114
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2182,f2120,f952,f7931]) ).
fof(f7931,plain,
( spl22_583
<=> ! [X4] :
( ~ empty(X4)
| sK15 = sK10(powerset(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_583])]) ).
fof(f2182,plain,
( ! [X4] :
( ~ empty(X4)
| sK15 = sK10(powerset(X4)) )
| ~ spl22_114
| ~ spl22_216 ),
inference(resolution,[],[f2121,f953]) ).
fof(f7916,plain,
( spl22_582
| ~ spl22_62
| ~ spl22_230 ),
inference(avatar_split_clause,[],[f2291,f2286,f598,f7914]) ).
fof(f7914,plain,
( spl22_582
<=> ! [X6,X7] :
( sK7(X6,X7) = apply(X6,sK8(X6,X7))
| apply(relation_dom_restriction(sK5,X7),sK7(X6,X7)) = apply(sK5,sK7(X6,X7))
| relation_rng(X6) = X7
| ~ sP1(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_582])]) ).
fof(f2291,plain,
( ! [X6,X7] :
( sK7(X6,X7) = apply(X6,sK8(X6,X7))
| apply(relation_dom_restriction(sK5,X7),sK7(X6,X7)) = apply(sK5,sK7(X6,X7))
| relation_rng(X6) = X7
| ~ sP1(X6) )
| ~ spl22_62
| ~ spl22_230 ),
inference(resolution,[],[f2287,f599]) ).
fof(f7912,plain,
( spl22_581
| ~ spl22_141
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2097,f2089,f1277,f7910]) ).
fof(f7910,plain,
( spl22_581
<=> ! [X13,X12] :
( sP0(X12,sK6(X13))
| apply(relation_dom_restriction(sK5,relation_dom(X12)),sK8(X12,sK6(X13))) = apply(sK5,sK8(X12,sK6(X13)))
| element(sK7(X12,sK6(X13)),X13)
| empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_581])]) ).
fof(f2097,plain,
( ! [X12,X13] :
( sP0(X12,sK6(X13))
| apply(relation_dom_restriction(sK5,relation_dom(X12)),sK8(X12,sK6(X13))) = apply(sK5,sK8(X12,sK6(X13)))
| element(sK7(X12,sK6(X13)),X13)
| empty(X13) )
| ~ spl22_141
| ~ spl22_212 ),
inference(resolution,[],[f2090,f1278]) ).
fof(f7908,plain,
( spl22_580
| ~ spl22_284
| ~ spl22_579 ),
inference(avatar_split_clause,[],[f7904,f7900,f3002,f7906]) ).
fof(f7906,plain,
( spl22_580
<=> ! [X1] :
( sP0(sK5,X1)
| apply(sK5,sK4) != sK7(sK5,X1)
| ~ in(apply(sK5,sK4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_580])]) ).
fof(f3002,plain,
( spl22_284
<=> sK5 = relation_dom_restriction(sK5,relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_284])]) ).
fof(f7900,plain,
( spl22_579
<=> ! [X1] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X1)
| ~ in(apply(sK5,sK4),X1)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_579])]) ).
fof(f7904,plain,
( ! [X1] :
( sP0(sK5,X1)
| apply(sK5,sK4) != sK7(sK5,X1)
| ~ in(apply(sK5,sK4),X1) )
| ~ spl22_284
| ~ spl22_579 ),
inference(forward_demodulation,[],[f7903,f3004]) ).
fof(f3004,plain,
( sK5 = relation_dom_restriction(sK5,relation_dom(sK5))
| ~ spl22_284 ),
inference(avatar_component_clause,[],[f3002]) ).
fof(f7903,plain,
( ! [X1] :
( apply(sK5,sK4) != sK7(sK5,X1)
| ~ in(apply(sK5,sK4),X1)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X1) )
| ~ spl22_284
| ~ spl22_579 ),
inference(forward_demodulation,[],[f7901,f3004]) ).
fof(f7901,plain,
( ! [X1] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X1)
| ~ in(apply(sK5,sK4),X1)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X1) )
| ~ spl22_579 ),
inference(avatar_component_clause,[],[f7900]) ).
fof(f7902,plain,
( ~ spl22_511
| spl22_579
| ~ spl22_80
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1662,f1591,f726,f7900,f7058]) ).
fof(f7058,plain,
( spl22_511
<=> in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_511])]) ).
fof(f1591,plain,
( spl22_175
<=> apply(sK5,sK4) = apply(relation_dom_restriction(sK5,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_175])]) ).
fof(f1662,plain,
( ! [X1] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X1)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ in(apply(sK5,sK4),X1) )
| ~ spl22_80
| ~ spl22_175 ),
inference(inner_rewriting,[],[f1660]) ).
fof(f1660,plain,
( ! [X1] :
( apply(sK5,sK4) != sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X1)
| sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ in(sK7(relation_dom_restriction(sK5,relation_dom(sK5)),X1),X1) )
| ~ spl22_80
| ~ spl22_175 ),
inference(superposition,[],[f727,f1593]) ).
fof(f1593,plain,
( apply(sK5,sK4) = apply(relation_dom_restriction(sK5,relation_dom(sK5)),sK4)
| ~ spl22_175 ),
inference(avatar_component_clause,[],[f1591]) ).
fof(f7852,plain,
( spl22_578
| ~ spl22_237
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7079,f7070,f2435,f7850]) ).
fof(f7850,plain,
( spl22_578
<=> ! [X8,X7] :
( ~ sP0(sK5,set_intersection2(X7,X8))
| in(apply(sK5,sK4),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_578])]) ).
fof(f7079,plain,
( ! [X8,X7] :
( ~ sP0(sK5,set_intersection2(X7,X8))
| in(apply(sK5,sK4),X8) )
| ~ spl22_237
| ~ spl22_513 ),
inference(resolution,[],[f7071,f2436]) ).
fof(f7786,plain,
( spl22_577
| ~ spl22_228
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2691,f2571,f2256,f7784]) ).
fof(f7784,plain,
( spl22_577
<=> ! [X82,X83,X84,X85] :
( ~ sP0(X82,X83)
| ~ empty(X83)
| sP2(relation_dom(X82),X84,X85)
| apply(relation_dom_restriction(sK5,X85),sK13(relation_dom(X82),X84,X85)) = apply(sK5,sK13(relation_dom(X82),X84,X85)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_577])]) ).
fof(f2691,plain,
( ! [X82,X83,X84,X85] :
( ~ sP0(X82,X83)
| ~ empty(X83)
| sP2(relation_dom(X82),X84,X85)
| apply(relation_dom_restriction(sK5,X85),sK13(relation_dom(X82),X84,X85)) = apply(sK5,sK13(relation_dom(X82),X84,X85)) )
| ~ spl22_228
| ~ spl22_250 ),
inference(resolution,[],[f2572,f2257]) ).
fof(f7782,plain,
( spl22_576
| ~ spl22_225
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2687,f2571,f2222,f7780]) ).
fof(f7780,plain,
( spl22_576
<=> ! [X68,X69,X67,X66] :
( ~ sP0(X66,X67)
| ~ empty(X67)
| sP2(X68,relation_dom(X66),X69)
| apply(relation_dom_restriction(sK5,X69),sK13(X68,relation_dom(X66),X69)) = apply(sK5,sK13(X68,relation_dom(X66),X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_576])]) ).
fof(f2687,plain,
( ! [X68,X69,X66,X67] :
( ~ sP0(X66,X67)
| ~ empty(X67)
| sP2(X68,relation_dom(X66),X69)
| apply(relation_dom_restriction(sK5,X69),sK13(X68,relation_dom(X66),X69)) = apply(sK5,sK13(X68,relation_dom(X66),X69)) )
| ~ spl22_225
| ~ spl22_250 ),
inference(resolution,[],[f2572,f2223]) ).
fof(f7778,plain,
( spl22_575
| ~ spl22_229
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2686,f2571,f2271,f7776]) ).
fof(f7776,plain,
( spl22_575
<=> ! [X62,X64,X63,X65] :
( ~ sP0(X62,X63)
| ~ empty(X63)
| sP2(X64,X65,relation_dom(X62))
| apply(sK5,sK13(X64,X65,relation_dom(X62))) = apply(relation_dom_restriction(sK5,X64),sK13(X64,X65,relation_dom(X62))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_575])]) ).
fof(f2686,plain,
( ! [X65,X62,X63,X64] :
( ~ sP0(X62,X63)
| ~ empty(X63)
| sP2(X64,X65,relation_dom(X62))
| apply(sK5,sK13(X64,X65,relation_dom(X62))) = apply(relation_dom_restriction(sK5,X64),sK13(X64,X65,relation_dom(X62))) )
| ~ spl22_229
| ~ spl22_250 ),
inference(resolution,[],[f2572,f2272]) ).
fof(f7774,plain,
( spl22_574
| ~ spl22_226
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2685,f2571,f2237,f7772]) ).
fof(f7772,plain,
( spl22_574
<=> ! [X61,X60,X59,X58] :
( ~ sP0(X58,X59)
| ~ empty(X59)
| sP2(X60,X61,relation_dom(X58))
| apply(sK5,sK13(X60,X61,relation_dom(X58))) = apply(relation_dom_restriction(sK5,X61),sK13(X60,X61,relation_dom(X58))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_574])]) ).
fof(f2685,plain,
( ! [X58,X59,X60,X61] :
( ~ sP0(X58,X59)
| ~ empty(X59)
| sP2(X60,X61,relation_dom(X58))
| apply(sK5,sK13(X60,X61,relation_dom(X58))) = apply(relation_dom_restriction(sK5,X61),sK13(X60,X61,relation_dom(X58))) )
| ~ spl22_226
| ~ spl22_250 ),
inference(resolution,[],[f2572,f2238]) ).
fof(f7770,plain,
( spl22_573
| ~ spl22_238
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7078,f7070,f2439,f7768]) ).
fof(f7768,plain,
( spl22_573
<=> ! [X6,X5] :
( ~ sP0(sK5,set_intersection2(X5,X6))
| in(apply(sK5,sK4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_573])]) ).
fof(f7078,plain,
( ! [X6,X5] :
( ~ sP0(sK5,set_intersection2(X5,X6))
| in(apply(sK5,sK4),X5) )
| ~ spl22_238
| ~ spl22_513 ),
inference(resolution,[],[f7071,f2440]) ).
fof(f7766,plain,
( spl22_572
| ~ spl22_131
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2282,f2271,f1173,f7764]) ).
fof(f7764,plain,
( spl22_572
<=> ! [X27,X28,X26] :
( sP2(X26,X27,sK10(powerset(X28)))
| apply(sK5,sK13(X26,X27,sK10(powerset(X28)))) = apply(relation_dom_restriction(sK5,X26),sK13(X26,X27,sK10(powerset(X28))))
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_572])]) ).
fof(f2282,plain,
( ! [X28,X26,X27] :
( sP2(X26,X27,sK10(powerset(X28)))
| apply(sK5,sK13(X26,X27,sK10(powerset(X28)))) = apply(relation_dom_restriction(sK5,X26),sK13(X26,X27,sK10(powerset(X28))))
| ~ empty(X28) )
| ~ spl22_131
| ~ spl22_229 ),
inference(resolution,[],[f2272,f1174]) ).
fof(f7762,plain,
( spl22_571
| ~ spl22_131
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2267,f2256,f1173,f7760]) ).
fof(f7760,plain,
( spl22_571
<=> ! [X25,X27,X26] :
( sP2(sK10(powerset(X25)),X26,X27)
| apply(relation_dom_restriction(sK5,X27),sK13(sK10(powerset(X25)),X26,X27)) = apply(sK5,sK13(sK10(powerset(X25)),X26,X27))
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_571])]) ).
fof(f2267,plain,
( ! [X26,X27,X25] :
( sP2(sK10(powerset(X25)),X26,X27)
| apply(relation_dom_restriction(sK5,X27),sK13(sK10(powerset(X25)),X26,X27)) = apply(sK5,sK13(sK10(powerset(X25)),X26,X27))
| ~ empty(X25) )
| ~ spl22_131
| ~ spl22_228 ),
inference(resolution,[],[f2257,f1174]) ).
fof(f7758,plain,
( spl22_570
| ~ spl22_131
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2248,f2237,f1173,f7756]) ).
fof(f7756,plain,
( spl22_570
<=> ! [X27,X28,X26] :
( sP2(X26,X27,sK10(powerset(X28)))
| apply(sK5,sK13(X26,X27,sK10(powerset(X28)))) = apply(relation_dom_restriction(sK5,X27),sK13(X26,X27,sK10(powerset(X28))))
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_570])]) ).
fof(f2248,plain,
( ! [X28,X26,X27] :
( sP2(X26,X27,sK10(powerset(X28)))
| apply(sK5,sK13(X26,X27,sK10(powerset(X28)))) = apply(relation_dom_restriction(sK5,X27),sK13(X26,X27,sK10(powerset(X28))))
| ~ empty(X28) )
| ~ spl22_131
| ~ spl22_226 ),
inference(resolution,[],[f2238,f1174]) ).
fof(f7754,plain,
( spl22_569
| ~ spl22_131
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2233,f2222,f1173,f7752]) ).
fof(f7752,plain,
( spl22_569
<=> ! [X25,X27,X26] :
( sP2(X25,sK10(powerset(X26)),X27)
| apply(relation_dom_restriction(sK5,X27),sK13(X25,sK10(powerset(X26)),X27)) = apply(sK5,sK13(X25,sK10(powerset(X26)),X27))
| ~ empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_569])]) ).
fof(f2233,plain,
( ! [X26,X27,X25] :
( sP2(X25,sK10(powerset(X26)),X27)
| apply(relation_dom_restriction(sK5,X27),sK13(X25,sK10(powerset(X26)),X27)) = apply(sK5,sK13(X25,sK10(powerset(X26)),X27))
| ~ empty(X26) )
| ~ spl22_131
| ~ spl22_225 ),
inference(resolution,[],[f2223,f1174]) ).
fof(f7655,plain,
( spl22_568
| ~ spl22_212
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2669,f2571,f2089,f7653]) ).
fof(f7653,plain,
( spl22_568
<=> ! [X6,X5,X7] :
( ~ sP0(X5,X6)
| ~ empty(X6)
| sP0(X7,relation_dom(X5))
| apply(relation_dom_restriction(sK5,relation_dom(X7)),sK8(X7,relation_dom(X5))) = apply(sK5,sK8(X7,relation_dom(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_568])]) ).
fof(f2669,plain,
( ! [X6,X7,X5] :
( ~ sP0(X5,X6)
| ~ empty(X6)
| sP0(X7,relation_dom(X5))
| apply(relation_dom_restriction(sK5,relation_dom(X7)),sK8(X7,relation_dom(X5))) = apply(sK5,sK8(X7,relation_dom(X5))) )
| ~ spl22_212
| ~ spl22_250 ),
inference(resolution,[],[f2572,f2090]) ).
fof(f7651,plain,
( spl22_567
| ~ spl22_228
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2427,f2331,f2256,f7649]) ).
fof(f7649,plain,
( spl22_567
<=> ! [X59,X60,X58] :
( ~ sP0(X58,sK15)
| sP2(relation_dom(X58),X59,X60)
| apply(relation_dom_restriction(sK5,X60),sK13(relation_dom(X58),X59,X60)) = apply(sK5,sK13(relation_dom(X58),X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_567])]) ).
fof(f2427,plain,
( ! [X58,X59,X60] :
( ~ sP0(X58,sK15)
| sP2(relation_dom(X58),X59,X60)
| apply(relation_dom_restriction(sK5,X60),sK13(relation_dom(X58),X59,X60)) = apply(sK5,sK13(relation_dom(X58),X59,X60)) )
| ~ spl22_228
| ~ spl22_236 ),
inference(resolution,[],[f2332,f2257]) ).
fof(f7644,plain,
( spl22_566
| ~ spl22_225
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2423,f2331,f2222,f7642]) ).
fof(f7642,plain,
( spl22_566
<=> ! [X48,X46,X47] :
( ~ sP0(X46,sK15)
| sP2(X47,relation_dom(X46),X48)
| apply(relation_dom_restriction(sK5,X48),sK13(X47,relation_dom(X46),X48)) = apply(sK5,sK13(X47,relation_dom(X46),X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_566])]) ).
fof(f2423,plain,
( ! [X48,X46,X47] :
( ~ sP0(X46,sK15)
| sP2(X47,relation_dom(X46),X48)
| apply(relation_dom_restriction(sK5,X48),sK13(X47,relation_dom(X46),X48)) = apply(sK5,sK13(X47,relation_dom(X46),X48)) )
| ~ spl22_225
| ~ spl22_236 ),
inference(resolution,[],[f2332,f2223]) ).
fof(f7640,plain,
( spl22_565
| ~ spl22_229
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2422,f2331,f2271,f7638]) ).
fof(f7638,plain,
( spl22_565
<=> ! [X45,X43,X44] :
( ~ sP0(X43,sK15)
| sP2(X44,X45,relation_dom(X43))
| apply(sK5,sK13(X44,X45,relation_dom(X43))) = apply(relation_dom_restriction(sK5,X44),sK13(X44,X45,relation_dom(X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_565])]) ).
fof(f2422,plain,
( ! [X44,X45,X43] :
( ~ sP0(X43,sK15)
| sP2(X44,X45,relation_dom(X43))
| apply(sK5,sK13(X44,X45,relation_dom(X43))) = apply(relation_dom_restriction(sK5,X44),sK13(X44,X45,relation_dom(X43))) )
| ~ spl22_229
| ~ spl22_236 ),
inference(resolution,[],[f2332,f2272]) ).
fof(f7636,plain,
( spl22_564
| ~ spl22_226
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2421,f2331,f2237,f7634]) ).
fof(f7634,plain,
( spl22_564
<=> ! [X41,X40,X42] :
( ~ sP0(X40,sK15)
| sP2(X41,X42,relation_dom(X40))
| apply(sK5,sK13(X41,X42,relation_dom(X40))) = apply(relation_dom_restriction(sK5,X42),sK13(X41,X42,relation_dom(X40))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_564])]) ).
fof(f2421,plain,
( ! [X40,X41,X42] :
( ~ sP0(X40,sK15)
| sP2(X41,X42,relation_dom(X40))
| apply(sK5,sK13(X41,X42,relation_dom(X40))) = apply(relation_dom_restriction(sK5,X42),sK13(X41,X42,relation_dom(X40))) )
| ~ spl22_226
| ~ spl22_236 ),
inference(resolution,[],[f2332,f2238]) ).
fof(f7632,plain,
( spl22_563
| ~ spl22_45
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2278,f2271,f448,f7630]) ).
fof(f7630,plain,
( spl22_563
<=> ! [X13,X14,X15] :
( sP2(X13,X14,X15)
| apply(sK5,sK13(X13,X14,X15)) = apply(relation_dom_restriction(sK5,X13),sK13(X13,X14,X15))
| ~ in(X15,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_563])]) ).
fof(f2278,plain,
( ! [X14,X15,X13] :
( sP2(X13,X14,X15)
| apply(sK5,sK13(X13,X14,X15)) = apply(relation_dom_restriction(sK5,X13),sK13(X13,X14,X15))
| ~ in(X15,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_229 ),
inference(resolution,[],[f2272,f449]) ).
fof(f7628,plain,
( spl22_562
| ~ spl22_46
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2277,f2271,f452,f7626]) ).
fof(f7626,plain,
( spl22_562
<=> ! [X11,X12,X10] :
( sP2(X10,X11,X12)
| apply(sK5,sK13(X10,X11,X12)) = apply(relation_dom_restriction(sK5,X10),sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_562])]) ).
fof(f2277,plain,
( ! [X10,X11,X12] :
( sP2(X10,X11,X12)
| apply(sK5,sK13(X10,X11,X12)) = apply(relation_dom_restriction(sK5,X10),sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X12) )
| ~ spl22_46
| ~ spl22_229 ),
inference(resolution,[],[f2272,f453]) ).
fof(f7624,plain,
( spl22_561
| ~ spl22_45
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2263,f2256,f448,f7622]) ).
fof(f7622,plain,
( spl22_561
<=> ! [X13,X12,X14] :
( sP2(X12,X13,X14)
| apply(relation_dom_restriction(sK5,X14),sK13(X12,X13,X14)) = apply(sK5,sK13(X12,X13,X14))
| ~ in(X12,sK13(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_561])]) ).
fof(f2263,plain,
( ! [X14,X12,X13] :
( sP2(X12,X13,X14)
| apply(relation_dom_restriction(sK5,X14),sK13(X12,X13,X14)) = apply(sK5,sK13(X12,X13,X14))
| ~ in(X12,sK13(X12,X13,X14)) )
| ~ spl22_45
| ~ spl22_228 ),
inference(resolution,[],[f2257,f449]) ).
fof(f7620,plain,
( spl22_560
| ~ spl22_46
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2262,f2256,f452,f7618]) ).
fof(f7618,plain,
( spl22_560
<=> ! [X9,X11,X10] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(sK5,X11),sK13(X9,X10,X11)) = apply(sK5,sK13(X9,X10,X11))
| element(sK13(X9,X10,X11),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_560])]) ).
fof(f2262,plain,
( ! [X10,X11,X9] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(sK5,X11),sK13(X9,X10,X11)) = apply(sK5,sK13(X9,X10,X11))
| element(sK13(X9,X10,X11),X9) )
| ~ spl22_46
| ~ spl22_228 ),
inference(resolution,[],[f2257,f453]) ).
fof(f7616,plain,
( spl22_559
| ~ spl22_45
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2244,f2237,f448,f7614]) ).
fof(f7614,plain,
( spl22_559
<=> ! [X13,X14,X15] :
( sP2(X13,X14,X15)
| apply(sK5,sK13(X13,X14,X15)) = apply(relation_dom_restriction(sK5,X14),sK13(X13,X14,X15))
| ~ in(X15,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_559])]) ).
fof(f2244,plain,
( ! [X14,X15,X13] :
( sP2(X13,X14,X15)
| apply(sK5,sK13(X13,X14,X15)) = apply(relation_dom_restriction(sK5,X14),sK13(X13,X14,X15))
| ~ in(X15,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_226 ),
inference(resolution,[],[f2238,f449]) ).
fof(f7612,plain,
( spl22_558
| ~ spl22_46
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2243,f2237,f452,f7610]) ).
fof(f7610,plain,
( spl22_558
<=> ! [X11,X12,X10] :
( sP2(X10,X11,X12)
| apply(sK5,sK13(X10,X11,X12)) = apply(relation_dom_restriction(sK5,X11),sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_558])]) ).
fof(f2243,plain,
( ! [X10,X11,X12] :
( sP2(X10,X11,X12)
| apply(sK5,sK13(X10,X11,X12)) = apply(relation_dom_restriction(sK5,X11),sK13(X10,X11,X12))
| element(sK13(X10,X11,X12),X12) )
| ~ spl22_46
| ~ spl22_226 ),
inference(resolution,[],[f2238,f453]) ).
fof(f7608,plain,
( spl22_557
| ~ spl22_45
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2229,f2222,f448,f7606]) ).
fof(f7606,plain,
( spl22_557
<=> ! [X13,X12,X14] :
( sP2(X12,X13,X14)
| apply(relation_dom_restriction(sK5,X14),sK13(X12,X13,X14)) = apply(sK5,sK13(X12,X13,X14))
| ~ in(X13,sK13(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_557])]) ).
fof(f2229,plain,
( ! [X14,X12,X13] :
( sP2(X12,X13,X14)
| apply(relation_dom_restriction(sK5,X14),sK13(X12,X13,X14)) = apply(sK5,sK13(X12,X13,X14))
| ~ in(X13,sK13(X12,X13,X14)) )
| ~ spl22_45
| ~ spl22_225 ),
inference(resolution,[],[f2223,f449]) ).
fof(f7604,plain,
( spl22_556
| ~ spl22_52
| ~ spl22_522 ),
inference(avatar_split_clause,[],[f7319,f7174,f498,f7602]) ).
fof(f7602,plain,
( spl22_556
<=> ! [X4] :
( ~ sP0(sK5,powerset(X4))
| subset(apply(sK5,sK4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_556])]) ).
fof(f7319,plain,
( ! [X4] :
( ~ sP0(sK5,powerset(X4))
| subset(apply(sK5,sK4),X4) )
| ~ spl22_52
| ~ spl22_522 ),
inference(resolution,[],[f7175,f499]) ).
fof(f7600,plain,
( spl22_555
| ~ spl22_46
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2228,f2222,f452,f7598]) ).
fof(f7598,plain,
( spl22_555
<=> ! [X9,X11,X10] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(sK5,X11),sK13(X9,X10,X11)) = apply(sK5,sK13(X9,X10,X11))
| element(sK13(X9,X10,X11),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_555])]) ).
fof(f2228,plain,
( ! [X10,X11,X9] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(sK5,X11),sK13(X9,X10,X11)) = apply(sK5,sK13(X9,X10,X11))
| element(sK13(X9,X10,X11),X10) )
| ~ spl22_46
| ~ spl22_225 ),
inference(resolution,[],[f2223,f453]) ).
fof(f7596,plain,
( spl22_554
| ~ spl22_131
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2099,f2089,f1173,f7594]) ).
fof(f7594,plain,
( spl22_554
<=> ! [X16,X17] :
( sP0(X16,sK10(powerset(X17)))
| apply(relation_dom_restriction(sK5,relation_dom(X16)),sK8(X16,sK10(powerset(X17)))) = apply(sK5,sK8(X16,sK10(powerset(X17))))
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_554])]) ).
fof(f2099,plain,
( ! [X16,X17] :
( sP0(X16,sK10(powerset(X17)))
| apply(relation_dom_restriction(sK5,relation_dom(X16)),sK8(X16,sK10(powerset(X17)))) = apply(sK5,sK8(X16,sK10(powerset(X17))))
| ~ empty(X17) )
| ~ spl22_131
| ~ spl22_212 ),
inference(resolution,[],[f2090,f1174]) ).
fof(f7550,plain,
( spl22_553
| ~ spl22_124
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2414,f2331,f1103,f7548]) ).
fof(f7548,plain,
( spl22_553
<=> ! [X21] :
( ~ sP0(X21,sK15)
| empty(relation_dom(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_553])]) ).
fof(f2414,plain,
( ! [X21] :
( ~ sP0(X21,sK15)
| empty(relation_dom(X21)) )
| ~ spl22_124
| ~ spl22_236 ),
inference(resolution,[],[f2332,f1104]) ).
fof(f7546,plain,
( spl22_552
| ~ spl22_29
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2180,f2120,f355,f7544]) ).
fof(f7544,plain,
( spl22_552
<=> ! [X1] :
( ~ empty(X1)
| relation(sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_552])]) ).
fof(f355,plain,
( spl22_29
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_29])]) ).
fof(f2180,plain,
( ! [X1] :
( ~ empty(X1)
| relation(sK10(powerset(X1))) )
| ~ spl22_29
| ~ spl22_216 ),
inference(resolution,[],[f2121,f356]) ).
fof(f356,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f7542,plain,
( spl22_551
| ~ spl22_28
| ~ spl22_216 ),
inference(avatar_split_clause,[],[f2179,f2120,f351,f7540]) ).
fof(f7540,plain,
( spl22_551
<=> ! [X0] :
( ~ empty(X0)
| function(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_551])]) ).
fof(f2179,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK10(powerset(X0))) )
| ~ spl22_28
| ~ spl22_216 ),
inference(resolution,[],[f2121,f352]) ).
fof(f7527,plain,
( spl22_550
| ~ spl22_212
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2405,f2331,f2089,f7525]) ).
fof(f7525,plain,
( spl22_550
<=> ! [X4,X3] :
( ~ sP0(X3,sK15)
| sP0(X4,relation_dom(X3))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,relation_dom(X3))) = apply(sK5,sK8(X4,relation_dom(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_550])]) ).
fof(f2405,plain,
( ! [X3,X4] :
( ~ sP0(X3,sK15)
| sP0(X4,relation_dom(X3))
| apply(relation_dom_restriction(sK5,relation_dom(X4)),sK8(X4,relation_dom(X3))) = apply(sK5,sK8(X4,relation_dom(X3))) )
| ~ spl22_212
| ~ spl22_236 ),
inference(resolution,[],[f2332,f2090]) ).
fof(f7507,plain,
( spl22_549
| ~ spl22_45
| ~ spl22_213 ),
inference(avatar_split_clause,[],[f2109,f2102,f448,f7505]) ).
fof(f7505,plain,
( spl22_549
<=> ! [X11,X10] :
( sP0(X10,X11)
| apply(relation_dom_restriction(sK5,X11),sK7(X10,X11)) = apply(sK5,sK7(X10,X11))
| ~ in(relation_dom(X10),sK8(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_549])]) ).
fof(f2109,plain,
( ! [X10,X11] :
( sP0(X10,X11)
| apply(relation_dom_restriction(sK5,X11),sK7(X10,X11)) = apply(sK5,sK7(X10,X11))
| ~ in(relation_dom(X10),sK8(X10,X11)) )
| ~ spl22_45
| ~ spl22_213 ),
inference(resolution,[],[f2103,f449]) ).
fof(f7503,plain,
( spl22_548
| ~ spl22_46
| ~ spl22_213 ),
inference(avatar_split_clause,[],[f2108,f2102,f452,f7501]) ).
fof(f7501,plain,
( spl22_548
<=> ! [X9,X8] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK5,X9),sK7(X8,X9)) = apply(sK5,sK7(X8,X9))
| element(sK8(X8,X9),relation_dom(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_548])]) ).
fof(f2108,plain,
( ! [X8,X9] :
( sP0(X8,X9)
| apply(relation_dom_restriction(sK5,X9),sK7(X8,X9)) = apply(sK5,sK7(X8,X9))
| element(sK8(X8,X9),relation_dom(X8)) )
| ~ spl22_46
| ~ spl22_213 ),
inference(resolution,[],[f2103,f453]) ).
fof(f7499,plain,
( spl22_547
| ~ spl22_45
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2095,f2089,f448,f7497]) ).
fof(f7497,plain,
( spl22_547
<=> ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK5,relation_dom(X7)),sK8(X7,X8)) = apply(sK5,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_547])]) ).
fof(f2095,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(sK5,relation_dom(X7)),sK8(X7,X8)) = apply(sK5,sK8(X7,X8))
| ~ in(X8,sK7(X7,X8)) )
| ~ spl22_45
| ~ spl22_212 ),
inference(resolution,[],[f2090,f449]) ).
fof(f7495,plain,
( spl22_546
| ~ spl22_46
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2094,f2089,f452,f7493]) ).
fof(f7493,plain,
( spl22_546
<=> ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK5,relation_dom(X5)),sK8(X5,X6)) = apply(sK5,sK8(X5,X6))
| element(sK7(X5,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_546])]) ).
fof(f2094,plain,
( ! [X6,X5] :
( sP0(X5,X6)
| apply(relation_dom_restriction(sK5,relation_dom(X5)),sK8(X5,X6)) = apply(sK5,sK8(X5,X6))
| element(sK7(X5,X6),X6) )
| ~ spl22_46
| ~ spl22_212 ),
inference(resolution,[],[f2090,f453]) ).
fof(f7468,plain,
( ~ spl22_545
| ~ spl22_513
| ~ spl22_530 ),
inference(avatar_split_clause,[],[f7423,f7257,f7070,f7465]) ).
fof(f7465,plain,
( spl22_545
<=> sP0(sK5,apply(sK5,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_545])]) ).
fof(f7257,plain,
( spl22_530
<=> ! [X4] :
( ~ sP0(sK5,X4)
| ~ in(X4,apply(sK5,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_530])]) ).
fof(f7423,plain,
( ~ sP0(sK5,apply(sK5,sK4))
| ~ spl22_513
| ~ spl22_530 ),
inference(duplicate_literal_removal,[],[f7357]) ).
fof(f7357,plain,
( ~ sP0(sK5,apply(sK5,sK4))
| ~ sP0(sK5,apply(sK5,sK4))
| ~ spl22_513
| ~ spl22_530 ),
inference(resolution,[],[f7258,f7071]) ).
fof(f7258,plain,
( ! [X4] :
( ~ in(X4,apply(sK5,sK4))
| ~ sP0(sK5,X4) )
| ~ spl22_530 ),
inference(avatar_component_clause,[],[f7257]) ).
fof(f7447,plain,
( ~ spl22_2
| spl22_544
| ~ spl22_1
| ~ spl22_392 ),
inference(avatar_split_clause,[],[f4993,f4946,f219,f7445,f224]) ).
fof(f7445,plain,
( spl22_544
<=> ! [X16,X17] :
( apply(relation_dom_restriction(sK5,X16),sK13(X16,X17,X16)) = apply(sK5,sK13(X16,X17,X16))
| sP2(X16,X17,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_544])]) ).
fof(f4993,plain,
( ! [X16,X17] :
( apply(relation_dom_restriction(sK5,X16),sK13(X16,X17,X16)) = apply(sK5,sK13(X16,X17,X16))
| ~ function(sK5)
| sP2(X16,X17,X16) )
| ~ spl22_1
| ~ spl22_392 ),
inference(resolution,[],[f4947,f221]) ).
fof(f7439,plain,
( ~ spl22_2
| spl22_543
| ~ spl22_1
| ~ spl22_391 ),
inference(avatar_split_clause,[],[f4974,f4942,f219,f7437,f224]) ).
fof(f7437,plain,
( spl22_543
<=> ! [X16,X17] :
( apply(relation_dom_restriction(sK5,X16),sK13(X17,X16,X16)) = apply(sK5,sK13(X17,X16,X16))
| sP2(X17,X16,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_543])]) ).
fof(f4974,plain,
( ! [X16,X17] :
( apply(relation_dom_restriction(sK5,X16),sK13(X17,X16,X16)) = apply(sK5,sK13(X17,X16,X16))
| ~ function(sK5)
| sP2(X17,X16,X16) )
| ~ spl22_1
| ~ spl22_391 ),
inference(resolution,[],[f4943,f221]) ).
fof(f7435,plain,
( spl22_542
| ~ spl22_213
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2674,f2571,f2102,f7433]) ).
fof(f7433,plain,
( spl22_542
<=> ! [X22,X20,X21] :
( ~ sP0(X20,X21)
| ~ empty(X21)
| sP0(X20,X22)
| apply(relation_dom_restriction(sK5,X22),sK7(X20,X22)) = apply(sK5,sK7(X20,X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_542])]) ).
fof(f2674,plain,
( ! [X21,X22,X20] :
( ~ sP0(X20,X21)
| ~ empty(X21)
| sP0(X20,X22)
| apply(relation_dom_restriction(sK5,X22),sK7(X20,X22)) = apply(sK5,sK7(X20,X22)) )
| ~ spl22_213
| ~ spl22_250 ),
inference(resolution,[],[f2572,f2103]) ).
fof(f7431,plain,
( spl22_541
| ~ spl22_41
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2275,f2271,f414,f7429]) ).
fof(f7429,plain,
( spl22_541
<=> ! [X4,X5,X3] :
( sP2(X3,X4,X5)
| apply(sK5,sK13(X3,X4,X5)) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,X5))
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_541])]) ).
fof(f2275,plain,
( ! [X3,X4,X5] :
( sP2(X3,X4,X5)
| apply(sK5,sK13(X3,X4,X5)) = apply(relation_dom_restriction(sK5,X3),sK13(X3,X4,X5))
| ~ empty(X5) )
| ~ spl22_41
| ~ spl22_229 ),
inference(resolution,[],[f2272,f415]) ).
fof(f7427,plain,
( spl22_540
| ~ spl22_41
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2260,f2256,f414,f7425]) ).
fof(f7425,plain,
( spl22_540
<=> ! [X4,X2,X3] :
( sP2(X2,X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X2,X3,X4)) = apply(sK5,sK13(X2,X3,X4))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_540])]) ).
fof(f2260,plain,
( ! [X2,X3,X4] :
( sP2(X2,X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X2,X3,X4)) = apply(sK5,sK13(X2,X3,X4))
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_228 ),
inference(resolution,[],[f2257,f415]) ).
fof(f7355,plain,
( spl22_539
| ~ spl22_41
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2241,f2237,f414,f7353]) ).
fof(f7353,plain,
( spl22_539
<=> ! [X4,X5,X3] :
( sP2(X3,X4,X5)
| apply(sK5,sK13(X3,X4,X5)) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,X5))
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_539])]) ).
fof(f2241,plain,
( ! [X3,X4,X5] :
( sP2(X3,X4,X5)
| apply(sK5,sK13(X3,X4,X5)) = apply(relation_dom_restriction(sK5,X4),sK13(X3,X4,X5))
| ~ empty(X5) )
| ~ spl22_41
| ~ spl22_226 ),
inference(resolution,[],[f2238,f415]) ).
fof(f7351,plain,
( spl22_538
| ~ spl22_41
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2226,f2222,f414,f7349]) ).
fof(f7349,plain,
( spl22_538
<=> ! [X4,X2,X3] :
( sP2(X2,X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X2,X3,X4)) = apply(sK5,sK13(X2,X3,X4))
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_538])]) ).
fof(f2226,plain,
( ! [X2,X3,X4] :
( sP2(X2,X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK13(X2,X3,X4)) = apply(sK5,sK13(X2,X3,X4))
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_225 ),
inference(resolution,[],[f2223,f415]) ).
fof(f7346,plain,
( spl22_537
| ~ spl22_284
| ~ spl22_536 ),
inference(avatar_split_clause,[],[f7342,f7339,f3002,f7344]) ).
fof(f7344,plain,
( spl22_537
<=> ! [X2,X3] :
( ~ sP0(sK5,X3)
| apply(sK5,sK4) != X2
| in(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_537])]) ).
fof(f7339,plain,
( spl22_536
<=> ! [X2,X3] :
( apply(sK5,sK4) != X2
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X3)
| in(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_536])]) ).
fof(f7342,plain,
( ! [X2,X3] :
( ~ sP0(sK5,X3)
| apply(sK5,sK4) != X2
| in(X2,X3) )
| ~ spl22_284
| ~ spl22_536 ),
inference(forward_demodulation,[],[f7340,f3004]) ).
fof(f7340,plain,
( ! [X2,X3] :
( apply(sK5,sK4) != X2
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X3)
| in(X2,X3) )
| ~ spl22_536 ),
inference(avatar_component_clause,[],[f7339]) ).
fof(f7341,plain,
( ~ spl22_511
| spl22_536
| ~ spl22_75
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1661,f1591,f678,f7339,f7058]) ).
fof(f1661,plain,
( ! [X2,X3] :
( apply(sK5,sK4) != X2
| in(X2,X3)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X3) )
| ~ spl22_75
| ~ spl22_175 ),
inference(superposition,[],[f679,f1593]) ).
fof(f7328,plain,
( spl22_535
| ~ spl22_36
| ~ spl22_242 ),
inference(avatar_split_clause,[],[f2543,f2456,f393,f7326]) ).
fof(f2456,plain,
( spl22_242
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_242])]) ).
fof(f2543,plain,
( ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_242 ),
inference(duplicate_literal_removal,[],[f2540]) ).
fof(f2540,plain,
( ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_242 ),
inference(resolution,[],[f2457,f394]) ).
fof(f2457,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_242 ),
inference(avatar_component_clause,[],[f2456]) ).
fof(f7324,plain,
( spl22_534
| ~ spl22_34
| ~ spl22_241 ),
inference(avatar_split_clause,[],[f2537,f2452,f385,f7322]) ).
fof(f7322,plain,
( spl22_534
<=> ! [X0] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_534])]) ).
fof(f2452,plain,
( spl22_241
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_241])]) ).
fof(f2537,plain,
( ! [X0] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_241 ),
inference(duplicate_literal_removal,[],[f2534]) ).
fof(f2534,plain,
( ! [X0] :
( one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_241 ),
inference(resolution,[],[f2453,f386]) ).
fof(f2453,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_241 ),
inference(avatar_component_clause,[],[f2452]) ).
fof(f7316,plain,
( spl22_533
| ~ spl22_36
| ~ spl22_219 ),
inference(avatar_split_clause,[],[f2201,f2148,f393,f7314]) ).
fof(f2201,plain,
( ! [X0] :
( sP0(X0,sK15)
| ~ empty(X0) )
| ~ spl22_36
| ~ spl22_219 ),
inference(resolution,[],[f2149,f394]) ).
fof(f7308,plain,
( ~ spl22_108
| spl22_532
| ~ spl22_125
| ~ spl22_196 ),
inference(avatar_split_clause,[],[f1951,f1921,f1107,f7305,f925]) ).
fof(f7305,plain,
( spl22_532
<=> sP0(sK15,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_532])]) ).
fof(f1951,plain,
( sP0(sK15,sK15)
| ~ sP1(sK15)
| ~ spl22_125
| ~ spl22_196 ),
inference(superposition,[],[f1108,f1923]) ).
fof(f7290,plain,
( spl22_531
| ~ spl22_4
| ~ spl22_396 ),
inference(avatar_split_clause,[],[f5223,f5075,f234,f7288]) ).
fof(f7288,plain,
( spl22_531
<=> ! [X6,X5] :
( ~ sP0(sK5,X5)
| apply(relation_dom_restriction(X6,X5),apply(sK5,sK4)) = apply(X6,apply(sK5,sK4))
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_531])]) ).
fof(f5223,plain,
( ! [X6,X5] :
( ~ sP0(sK5,X5)
| apply(relation_dom_restriction(X6,X5),apply(sK5,sK4)) = apply(X6,apply(sK5,sK4))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_4
| ~ spl22_396 ),
inference(resolution,[],[f5076,f236]) ).
fof(f236,plain,
( in(sK4,relation_dom(sK5))
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f7259,plain,
( spl22_530
| ~ spl22_45
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7077,f7070,f448,f7257]) ).
fof(f7077,plain,
( ! [X4] :
( ~ sP0(sK5,X4)
| ~ in(X4,apply(sK5,sK4)) )
| ~ spl22_45
| ~ spl22_513 ),
inference(resolution,[],[f7071,f449]) ).
fof(f7204,plain,
( ~ spl22_2
| spl22_529
| ~ spl22_1
| ~ spl22_366 ),
inference(avatar_split_clause,[],[f4284,f4135,f219,f7202,f224]) ).
fof(f7202,plain,
( spl22_529
<=> ! [X11] :
( empty(X11)
| empty(powerset(X11))
| apply(relation_dom_restriction(sK5,powerset(X11)),sK6(X11)) = apply(sK5,sK6(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_529])]) ).
fof(f4284,plain,
( ! [X11] :
( empty(X11)
| apply(relation_dom_restriction(sK5,powerset(X11)),sK6(X11)) = apply(sK5,sK6(X11))
| ~ function(sK5)
| empty(powerset(X11)) )
| ~ spl22_1
| ~ spl22_366 ),
inference(resolution,[],[f4136,f221]) ).
fof(f7200,plain,
( spl22_528
| ~ spl22_213
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2410,f2331,f2102,f7198]) ).
fof(f7198,plain,
( spl22_528
<=> ! [X13,X14] :
( ~ sP0(X13,sK15)
| sP0(X13,X14)
| apply(relation_dom_restriction(sK5,X14),sK7(X13,X14)) = apply(sK5,sK7(X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_528])]) ).
fof(f2410,plain,
( ! [X14,X13] :
( ~ sP0(X13,sK15)
| sP0(X13,X14)
| apply(relation_dom_restriction(sK5,X14),sK7(X13,X14)) = apply(sK5,sK7(X13,X14)) )
| ~ spl22_213
| ~ spl22_236 ),
inference(resolution,[],[f2332,f2103]) ).
fof(f7196,plain,
( spl22_527
| ~ spl22_116
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f2283,f2271,f959,f7194]) ).
fof(f7194,plain,
( spl22_527
<=> ! [X29,X30] :
( sP2(X29,X30,sK15)
| apply(sK5,sK13(X29,X30,sK15)) = apply(relation_dom_restriction(sK5,X29),sK13(X29,X30,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_527])]) ).
fof(f2283,plain,
( ! [X29,X30] :
( sP2(X29,X30,sK15)
| apply(sK5,sK13(X29,X30,sK15)) = apply(relation_dom_restriction(sK5,X29),sK13(X29,X30,sK15)) )
| ~ spl22_116
| ~ spl22_229 ),
inference(resolution,[],[f2272,f960]) ).
fof(f7192,plain,
( spl22_526
| ~ spl22_116
| ~ spl22_228 ),
inference(avatar_split_clause,[],[f2268,f2256,f959,f7190]) ).
fof(f7190,plain,
( spl22_526
<=> ! [X29,X28] :
( sP2(sK15,X28,X29)
| apply(relation_dom_restriction(sK5,X29),sK13(sK15,X28,X29)) = apply(sK5,sK13(sK15,X28,X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_526])]) ).
fof(f2268,plain,
( ! [X28,X29] :
( sP2(sK15,X28,X29)
| apply(relation_dom_restriction(sK5,X29),sK13(sK15,X28,X29)) = apply(sK5,sK13(sK15,X28,X29)) )
| ~ spl22_116
| ~ spl22_228 ),
inference(resolution,[],[f2257,f960]) ).
fof(f7188,plain,
( spl22_525
| ~ spl22_116
| ~ spl22_226 ),
inference(avatar_split_clause,[],[f2249,f2237,f959,f7186]) ).
fof(f7186,plain,
( spl22_525
<=> ! [X29,X30] :
( sP2(X29,X30,sK15)
| apply(sK5,sK13(X29,X30,sK15)) = apply(relation_dom_restriction(sK5,X30),sK13(X29,X30,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_525])]) ).
fof(f2249,plain,
( ! [X29,X30] :
( sP2(X29,X30,sK15)
| apply(sK5,sK13(X29,X30,sK15)) = apply(relation_dom_restriction(sK5,X30),sK13(X29,X30,sK15)) )
| ~ spl22_116
| ~ spl22_226 ),
inference(resolution,[],[f2238,f960]) ).
fof(f7184,plain,
( spl22_524
| ~ spl22_116
| ~ spl22_225 ),
inference(avatar_split_clause,[],[f2234,f2222,f959,f7182]) ).
fof(f7182,plain,
( spl22_524
<=> ! [X29,X28] :
( sP2(X28,sK15,X29)
| apply(relation_dom_restriction(sK5,X29),sK13(X28,sK15,X29)) = apply(sK5,sK13(X28,sK15,X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_524])]) ).
fof(f2234,plain,
( ! [X28,X29] :
( sP2(X28,sK15,X29)
| apply(relation_dom_restriction(sK5,X29),sK13(X28,sK15,X29)) = apply(sK5,sK13(X28,sK15,X29)) )
| ~ spl22_116
| ~ spl22_225 ),
inference(resolution,[],[f2223,f960]) ).
fof(f7180,plain,
( spl22_523
| ~ spl22_41
| ~ spl22_213 ),
inference(avatar_split_clause,[],[f2106,f2102,f414,f7178]) ).
fof(f7178,plain,
( spl22_523
<=> ! [X4,X3] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK7(X3,X4)) = apply(sK5,sK7(X3,X4))
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_523])]) ).
fof(f2106,plain,
( ! [X3,X4] :
( sP0(X3,X4)
| apply(relation_dom_restriction(sK5,X4),sK7(X3,X4)) = apply(sK5,sK7(X3,X4))
| ~ empty(relation_dom(X3)) )
| ~ spl22_41
| ~ spl22_213 ),
inference(resolution,[],[f2103,f415]) ).
fof(f7176,plain,
( spl22_522
| ~ spl22_46
| ~ spl22_513 ),
inference(avatar_split_clause,[],[f7076,f7070,f452,f7174]) ).
fof(f7076,plain,
( ! [X3] :
( ~ sP0(sK5,X3)
| element(apply(sK5,sK4),X3) )
| ~ spl22_46
| ~ spl22_513 ),
inference(resolution,[],[f7071,f453]) ).
fof(f7172,plain,
( spl22_521
| ~ spl22_41
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2092,f2089,f414,f7170]) ).
fof(f7170,plain,
( spl22_521
<=> ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_521])]) ).
fof(f2092,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(sK5,relation_dom(X0)),sK8(X0,X1)) = apply(sK5,sK8(X0,X1))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_212 ),
inference(resolution,[],[f2090,f415]) ).
fof(f7149,plain,
( spl22_520
| ~ spl22_58
| ~ spl22_206 ),
inference(avatar_split_clause,[],[f2022,f2018,f548,f7147]) ).
fof(f7147,plain,
( spl22_520
<=> ! [X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_520])]) ).
fof(f2018,plain,
( spl22_206
<=> ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| apply(relation_dom_restriction(X4,X5),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X4,X5),relation_dom(sK5)),sK4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_206])]) ).
fof(f2022,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_206 ),
inference(duplicate_literal_removal,[],[f2021]) ).
fof(f2021,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(X0,X1),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_206 ),
inference(resolution,[],[f2019,f549]) ).
fof(f2019,plain,
( ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| apply(relation_dom_restriction(X4,X5),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X4,X5),relation_dom(sK5)),sK4)
| ~ relation(X4) )
| ~ spl22_206 ),
inference(avatar_component_clause,[],[f2018]) ).
fof(f7145,plain,
( ~ spl22_518
| spl22_519
| ~ spl22_153
| ~ spl22_192 ),
inference(avatar_split_clause,[],[f1900,f1896,f1395,f7143,f7139]) ).
fof(f7139,plain,
( spl22_518
<=> in(sK4,relation_dom(relation_dom_restriction(sK15,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_518])]) ).
fof(f7143,plain,
( spl22_519
<=> ! [X0] :
( in(apply(sK15,sK4),X0)
| ~ sP0(relation_dom_restriction(sK15,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_519])]) ).
fof(f1896,plain,
( spl22_192
<=> apply(sK15,sK4) = apply(relation_dom_restriction(sK15,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_192])]) ).
fof(f1900,plain,
( ! [X0] :
( in(apply(sK15,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK15,relation_dom(sK5))))
| ~ sP0(relation_dom_restriction(sK15,relation_dom(sK5)),X0) )
| ~ spl22_153
| ~ spl22_192 ),
inference(superposition,[],[f1396,f1898]) ).
fof(f1898,plain,
( apply(sK15,sK4) = apply(relation_dom_restriction(sK15,relation_dom(sK5)),sK4)
| ~ spl22_192 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f7137,plain,
( ~ spl22_516
| spl22_517
| ~ spl22_153
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f1891,f1887,f1395,f7135,f7131]) ).
fof(f7131,plain,
( spl22_516
<=> in(sK4,relation_dom(relation_dom_restriction(sK20,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_516])]) ).
fof(f7135,plain,
( spl22_517
<=> ! [X0] :
( in(apply(sK20,sK4),X0)
| ~ sP0(relation_dom_restriction(sK20,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_517])]) ).
fof(f1887,plain,
( spl22_191
<=> apply(sK20,sK4) = apply(relation_dom_restriction(sK20,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_191])]) ).
fof(f1891,plain,
( ! [X0] :
( in(apply(sK20,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK20,relation_dom(sK5))))
| ~ sP0(relation_dom_restriction(sK20,relation_dom(sK5)),X0) )
| ~ spl22_153
| ~ spl22_191 ),
inference(superposition,[],[f1396,f1889]) ).
fof(f1889,plain,
( apply(sK20,sK4) = apply(relation_dom_restriction(sK20,relation_dom(sK5)),sK4)
| ~ spl22_191 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f7129,plain,
( ~ spl22_514
| spl22_515
| ~ spl22_153
| ~ spl22_184 ),
inference(avatar_split_clause,[],[f1787,f1693,f1395,f7127,f7123]) ).
fof(f7123,plain,
( spl22_514
<=> in(sK4,relation_dom(relation_dom_restriction(sK19,relation_dom(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_514])]) ).
fof(f7127,plain,
( spl22_515
<=> ! [X0] :
( in(apply(sK19,sK4),X0)
| ~ sP0(relation_dom_restriction(sK19,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_515])]) ).
fof(f1693,plain,
( spl22_184
<=> apply(sK19,sK4) = apply(relation_dom_restriction(sK19,relation_dom(sK5)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_184])]) ).
fof(f1787,plain,
( ! [X0] :
( in(apply(sK19,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK19,relation_dom(sK5))))
| ~ sP0(relation_dom_restriction(sK19,relation_dom(sK5)),X0) )
| ~ spl22_153
| ~ spl22_184 ),
inference(superposition,[],[f1396,f1695]) ).
fof(f1695,plain,
( apply(sK19,sK4) = apply(relation_dom_restriction(sK19,relation_dom(sK5)),sK4)
| ~ spl22_184 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f7072,plain,
( spl22_513
| ~ spl22_284
| ~ spl22_512 ),
inference(avatar_split_clause,[],[f7067,f7062,f3002,f7070]) ).
fof(f7062,plain,
( spl22_512
<=> ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_512])]) ).
fof(f7067,plain,
( ! [X0] :
( ~ sP0(sK5,X0)
| in(apply(sK5,sK4),X0) )
| ~ spl22_284
| ~ spl22_512 ),
inference(forward_demodulation,[],[f7063,f3004]) ).
fof(f7063,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_512 ),
inference(avatar_component_clause,[],[f7062]) ).
fof(f7066,plain,
( ~ spl22_4
| ~ spl22_284
| spl22_511 ),
inference(avatar_split_clause,[],[f7065,f7058,f3002,f234]) ).
fof(f7065,plain,
( ~ in(sK4,relation_dom(sK5))
| ~ spl22_284
| spl22_511 ),
inference(forward_demodulation,[],[f7060,f3004]) ).
fof(f7060,plain,
( ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| spl22_511 ),
inference(avatar_component_clause,[],[f7058]) ).
fof(f7064,plain,
( ~ spl22_511
| spl22_512
| ~ spl22_153
| ~ spl22_175 ),
inference(avatar_split_clause,[],[f1659,f1591,f1395,f7062,f7058]) ).
fof(f1659,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,relation_dom(sK5))))
| ~ sP0(relation_dom_restriction(sK5,relation_dom(sK5)),X0) )
| ~ spl22_153
| ~ spl22_175 ),
inference(superposition,[],[f1396,f1593]) ).
fof(f7032,plain,
( spl22_510
| ~ spl22_116
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f2100,f2089,f959,f7030]) ).
fof(f7030,plain,
( spl22_510
<=> ! [X18] :
( sP0(X18,sK15)
| apply(relation_dom_restriction(sK5,relation_dom(X18)),sK8(X18,sK15)) = apply(sK5,sK8(X18,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_510])]) ).
fof(f2100,plain,
( ! [X18] :
( sP0(X18,sK15)
| apply(relation_dom_restriction(sK5,relation_dom(X18)),sK8(X18,sK15)) = apply(sK5,sK8(X18,sK15)) )
| ~ spl22_116
| ~ spl22_212 ),
inference(resolution,[],[f2090,f960]) ).
fof(f7028,plain,
( spl22_509
| ~ spl22_58
| ~ spl22_204 ),
inference(avatar_split_clause,[],[f2012,f2008,f548,f7026]) ).
fof(f7026,plain,
( spl22_509
<=> ! [X0,X1] :
( apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_509])]) ).
fof(f2008,plain,
( spl22_204
<=> ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| apply(relation_dom_restriction(relation_dom_restriction(X4,X5),sK3),sK4) = apply(relation_dom_restriction(X4,X5),sK4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_204])]) ).
fof(f2012,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_204 ),
inference(duplicate_literal_removal,[],[f2011]) ).
fof(f2011,plain,
( ! [X0,X1] :
( apply(relation_dom_restriction(relation_dom_restriction(X0,X1),sK3),sK4) = apply(relation_dom_restriction(X0,X1),sK4)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_204 ),
inference(resolution,[],[f2009,f549]) ).
fof(f2009,plain,
( ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| apply(relation_dom_restriction(relation_dom_restriction(X4,X5),sK3),sK4) = apply(relation_dom_restriction(X4,X5),sK4)
| ~ relation(X4) )
| ~ spl22_204 ),
inference(avatar_component_clause,[],[f2008]) ).
fof(f7024,plain,
( ~ spl22_507
| spl22_508
| ~ spl22_139
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1435,f1395,f1268,f7022,f7018]) ).
fof(f7018,plain,
( spl22_507
<=> in(sK4,relation_dom(relation_dom_restriction(sK20,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_507])]) ).
fof(f7022,plain,
( spl22_508
<=> ! [X3] :
( in(apply(sK20,sK4),X3)
| ~ sP0(relation_dom_restriction(sK20,sK3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_508])]) ).
fof(f1268,plain,
( spl22_139
<=> apply(relation_dom_restriction(sK20,sK3),sK4) = apply(sK20,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_139])]) ).
fof(f1435,plain,
( ! [X3] :
( in(apply(sK20,sK4),X3)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK20,sK3)))
| ~ sP0(relation_dom_restriction(sK20,sK3),X3) )
| ~ spl22_139
| ~ spl22_153 ),
inference(superposition,[],[f1396,f1270]) ).
fof(f1270,plain,
( apply(relation_dom_restriction(sK20,sK3),sK4) = apply(sK20,sK4)
| ~ spl22_139 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f7016,plain,
( ~ spl22_505
| spl22_506
| ~ spl22_128
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1434,f1395,f1160,f7014,f7010]) ).
fof(f7010,plain,
( spl22_505
<=> in(sK4,relation_dom(relation_dom_restriction(sK19,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_505])]) ).
fof(f7014,plain,
( spl22_506
<=> ! [X2] :
( in(apply(sK19,sK4),X2)
| ~ sP0(relation_dom_restriction(sK19,sK3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_506])]) ).
fof(f1160,plain,
( spl22_128
<=> apply(relation_dom_restriction(sK19,sK3),sK4) = apply(sK19,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_128])]) ).
fof(f1434,plain,
( ! [X2] :
( in(apply(sK19,sK4),X2)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK19,sK3)))
| ~ sP0(relation_dom_restriction(sK19,sK3),X2) )
| ~ spl22_128
| ~ spl22_153 ),
inference(superposition,[],[f1396,f1162]) ).
fof(f1162,plain,
( apply(relation_dom_restriction(sK19,sK3),sK4) = apply(sK19,sK4)
| ~ spl22_128 ),
inference(avatar_component_clause,[],[f1160]) ).
fof(f7008,plain,
( spl22_504
| ~ spl22_25
| ~ spl22_499 ),
inference(avatar_split_clause,[],[f6965,f6962,f339,f7006]) ).
fof(f7006,plain,
( spl22_504
<=> ! [X0] : apply(sK5,sK15) = apply(relation_dom_restriction(sK5,powerset(X0)),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_504])]) ).
fof(f339,plain,
( spl22_25
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_25])]) ).
fof(f6962,plain,
( spl22_499
<=> ! [X11] :
( apply(relation_dom_restriction(sK5,powerset(X11)),sK15) = apply(sK5,sK15)
| empty(powerset(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_499])]) ).
fof(f6965,plain,
( ! [X0] : apply(sK5,sK15) = apply(relation_dom_restriction(sK5,powerset(X0)),sK15)
| ~ spl22_25
| ~ spl22_499 ),
inference(resolution,[],[f6963,f340]) ).
fof(f340,plain,
( ! [X0] : ~ empty(powerset(X0))
| ~ spl22_25 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f6963,plain,
( ! [X11] :
( empty(powerset(X11))
| apply(relation_dom_restriction(sK5,powerset(X11)),sK15) = apply(sK5,sK15) )
| ~ spl22_499 ),
inference(avatar_component_clause,[],[f6962]) ).
fof(f7004,plain,
( ~ spl22_502
| spl22_503
| ~ spl22_151
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1433,f1395,f1372,f7002,f6998]) ).
fof(f6998,plain,
( spl22_502
<=> in(sK4,relation_dom(relation_dom_restriction(sK15,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_502])]) ).
fof(f7002,plain,
( spl22_503
<=> ! [X1] :
( in(apply(sK15,sK4),X1)
| ~ sP0(relation_dom_restriction(sK15,sK3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_503])]) ).
fof(f1372,plain,
( spl22_151
<=> apply(relation_dom_restriction(sK15,sK3),sK4) = apply(sK15,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_151])]) ).
fof(f1433,plain,
( ! [X1] :
( in(apply(sK15,sK4),X1)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK15,sK3)))
| ~ sP0(relation_dom_restriction(sK15,sK3),X1) )
| ~ spl22_151
| ~ spl22_153 ),
inference(superposition,[],[f1396,f1374]) ).
fof(f1374,plain,
( apply(relation_dom_restriction(sK15,sK3),sK4) = apply(sK15,sK4)
| ~ spl22_151 ),
inference(avatar_component_clause,[],[f1372]) ).
fof(f6996,plain,
( ~ spl22_500
| spl22_501
| ~ spl22_117
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1432,f1395,f1062,f6994,f6990]) ).
fof(f1432,plain,
( ! [X0] :
( in(apply(sK5,sK4),X0)
| ~ in(sK4,relation_dom(relation_dom_restriction(sK5,sK3)))
| ~ sP0(relation_dom_restriction(sK5,sK3),X0) )
| ~ spl22_117
| ~ spl22_153 ),
inference(superposition,[],[f1396,f1064]) ).
fof(f6964,plain,
( ~ spl22_2
| spl22_499
| ~ spl22_1
| ~ spl22_342 ),
inference(avatar_split_clause,[],[f3790,f3750,f219,f6962,f224]) ).
fof(f3790,plain,
( ! [X11] :
( apply(relation_dom_restriction(sK5,powerset(X11)),sK15) = apply(sK5,sK15)
| ~ function(sK5)
| empty(powerset(X11)) )
| ~ spl22_1
| ~ spl22_342 ),
inference(resolution,[],[f3751,f221]) ).
fof(f6921,plain,
( ~ spl22_2
| spl22_498
| ~ spl22_1
| ~ spl22_341 ),
inference(avatar_split_clause,[],[f3771,f3746,f219,f6919,f224]) ).
fof(f3771,plain,
( ! [X11] :
( apply(relation_dom_restriction(sK5,X11),sK10(X11)) = apply(sK5,sK10(X11))
| ~ function(sK5)
| empty(X11) )
| ~ spl22_1
| ~ spl22_341 ),
inference(resolution,[],[f3747,f221]) ).
fof(f6908,plain,
( spl22_497
| ~ spl22_79
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1747,f1741,f718,f6906]) ).
fof(f6906,plain,
( spl22_497
<=> ! [X12,X11,X10] :
( apply(relation_dom_restriction(X10,X11),sK7(X12,relation_dom(relation_dom_restriction(X10,X11)))) = apply(X10,sK7(X12,relation_dom(relation_dom_restriction(X10,X11))))
| ~ function(X10)
| ~ relation(X10)
| ~ function(relation_dom_restriction(X10,X11))
| ~ relation(relation_dom_restriction(X10,X11))
| sK7(X12,relation_dom(relation_dom_restriction(X10,X11))) = apply(X12,sK8(X12,relation_dom(relation_dom_restriction(X10,X11))))
| sP0(X12,relation_dom(relation_dom_restriction(X10,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_497])]) ).
fof(f1747,plain,
( ! [X10,X11,X12] :
( apply(relation_dom_restriction(X10,X11),sK7(X12,relation_dom(relation_dom_restriction(X10,X11)))) = apply(X10,sK7(X12,relation_dom(relation_dom_restriction(X10,X11))))
| ~ function(X10)
| ~ relation(X10)
| ~ function(relation_dom_restriction(X10,X11))
| ~ relation(relation_dom_restriction(X10,X11))
| sK7(X12,relation_dom(relation_dom_restriction(X10,X11))) = apply(X12,sK8(X12,relation_dom(relation_dom_restriction(X10,X11))))
| sP0(X12,relation_dom(relation_dom_restriction(X10,X11))) )
| ~ spl22_79
| ~ spl22_185 ),
inference(resolution,[],[f1742,f719]) ).
fof(f6715,plain,
( spl22_496
| ~ spl22_146
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1766,f1741,f1316,f6713]) ).
fof(f6713,plain,
( spl22_496
<=> ! [X80,X78,X79] :
( apply(relation_dom_restriction(X78,X79),sK13(relation_dom(relation_dom_restriction(X78,X79)),X80,relation_dom(relation_dom_restriction(X78,X79)))) = apply(X78,sK13(relation_dom(relation_dom_restriction(X78,X79)),X80,relation_dom(relation_dom_restriction(X78,X79))))
| ~ function(X78)
| ~ relation(X78)
| ~ function(relation_dom_restriction(X78,X79))
| ~ relation(relation_dom_restriction(X78,X79))
| sP2(relation_dom(relation_dom_restriction(X78,X79)),X80,relation_dom(relation_dom_restriction(X78,X79))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_496])]) ).
fof(f1766,plain,
( ! [X80,X78,X79] :
( apply(relation_dom_restriction(X78,X79),sK13(relation_dom(relation_dom_restriction(X78,X79)),X80,relation_dom(relation_dom_restriction(X78,X79)))) = apply(X78,sK13(relation_dom(relation_dom_restriction(X78,X79)),X80,relation_dom(relation_dom_restriction(X78,X79))))
| ~ function(X78)
| ~ relation(X78)
| ~ function(relation_dom_restriction(X78,X79))
| ~ relation(relation_dom_restriction(X78,X79))
| sP2(relation_dom(relation_dom_restriction(X78,X79)),X80,relation_dom(relation_dom_restriction(X78,X79))) )
| ~ spl22_146
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1317]) ).
fof(f6711,plain,
( spl22_495
| ~ spl22_145
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1765,f1741,f1312,f6709]) ).
fof(f6709,plain,
( spl22_495
<=> ! [X77,X75,X76] :
( apply(relation_dom_restriction(X75,X76),sK13(X77,relation_dom(relation_dom_restriction(X75,X76)),relation_dom(relation_dom_restriction(X75,X76)))) = apply(X75,sK13(X77,relation_dom(relation_dom_restriction(X75,X76)),relation_dom(relation_dom_restriction(X75,X76))))
| ~ function(X75)
| ~ relation(X75)
| ~ function(relation_dom_restriction(X75,X76))
| ~ relation(relation_dom_restriction(X75,X76))
| sP2(X77,relation_dom(relation_dom_restriction(X75,X76)),relation_dom(relation_dom_restriction(X75,X76))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_495])]) ).
fof(f1765,plain,
( ! [X76,X77,X75] :
( apply(relation_dom_restriction(X75,X76),sK13(X77,relation_dom(relation_dom_restriction(X75,X76)),relation_dom(relation_dom_restriction(X75,X76)))) = apply(X75,sK13(X77,relation_dom(relation_dom_restriction(X75,X76)),relation_dom(relation_dom_restriction(X75,X76))))
| ~ function(X75)
| ~ relation(X75)
| ~ function(relation_dom_restriction(X75,X76))
| ~ relation(relation_dom_restriction(X75,X76))
| sP2(X77,relation_dom(relation_dom_restriction(X75,X76)),relation_dom(relation_dom_restriction(X75,X76))) )
| ~ spl22_145
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1313]) ).
fof(f6707,plain,
( spl22_494
| ~ spl22_78
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1764,f1741,f692,f6705]) ).
fof(f6705,plain,
( spl22_494
<=> ! [X74,X71,X73,X72] :
( apply(relation_dom_restriction(X71,X72),sK13(relation_dom(relation_dom_restriction(X71,X72)),X73,X74)) = apply(X71,sK13(relation_dom(relation_dom_restriction(X71,X72)),X73,X74))
| ~ function(X71)
| ~ relation(X71)
| ~ function(relation_dom_restriction(X71,X72))
| ~ relation(relation_dom_restriction(X71,X72))
| in(sK13(relation_dom(relation_dom_restriction(X71,X72)),X73,X74),X74)
| sP2(relation_dom(relation_dom_restriction(X71,X72)),X73,X74) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_494])]) ).
fof(f1764,plain,
( ! [X72,X73,X71,X74] :
( apply(relation_dom_restriction(X71,X72),sK13(relation_dom(relation_dom_restriction(X71,X72)),X73,X74)) = apply(X71,sK13(relation_dom(relation_dom_restriction(X71,X72)),X73,X74))
| ~ function(X71)
| ~ relation(X71)
| ~ function(relation_dom_restriction(X71,X72))
| ~ relation(relation_dom_restriction(X71,X72))
| in(sK13(relation_dom(relation_dom_restriction(X71,X72)),X73,X74),X74)
| sP2(relation_dom(relation_dom_restriction(X71,X72)),X73,X74) )
| ~ spl22_78
| ~ spl22_185 ),
inference(resolution,[],[f1742,f693]) ).
fof(f6703,plain,
( spl22_493
| ~ spl22_170
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1762,f1741,f1550,f6701]) ).
fof(f6701,plain,
( spl22_493
<=> ! [X65,X64,X63,X66] :
( apply(relation_dom_restriction(X63,X64),sK13(relation_dom(relation_dom_restriction(X63,X64)),X65,X66)) = apply(X63,sK13(relation_dom(relation_dom_restriction(X63,X64)),X65,X66))
| ~ function(X63)
| ~ relation(X63)
| ~ function(relation_dom_restriction(X63,X64))
| ~ relation(relation_dom_restriction(X63,X64))
| element(sK13(relation_dom(relation_dom_restriction(X63,X64)),X65,X66),X66)
| sP2(relation_dom(relation_dom_restriction(X63,X64)),X65,X66) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_493])]) ).
fof(f1762,plain,
( ! [X65,X63,X66,X64] :
( apply(relation_dom_restriction(X63,X64),sK13(relation_dom(relation_dom_restriction(X63,X64)),X65,X66)) = apply(X63,sK13(relation_dom(relation_dom_restriction(X63,X64)),X65,X66))
| ~ function(X63)
| ~ relation(X63)
| ~ function(relation_dom_restriction(X63,X64))
| ~ relation(relation_dom_restriction(X63,X64))
| element(sK13(relation_dom(relation_dom_restriction(X63,X64)),X65,X66),X66)
| sP2(relation_dom(relation_dom_restriction(X63,X64)),X65,X66) )
| ~ spl22_170
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1551]) ).
fof(f6699,plain,
( spl22_492
| ~ spl22_77
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1761,f1741,f688,f6697]) ).
fof(f6697,plain,
( spl22_492
<=> ! [X61,X60,X59,X62] :
( apply(relation_dom_restriction(X59,X60),sK13(X61,relation_dom(relation_dom_restriction(X59,X60)),X62)) = apply(X59,sK13(X61,relation_dom(relation_dom_restriction(X59,X60)),X62))
| ~ function(X59)
| ~ relation(X59)
| ~ function(relation_dom_restriction(X59,X60))
| ~ relation(relation_dom_restriction(X59,X60))
| in(sK13(X61,relation_dom(relation_dom_restriction(X59,X60)),X62),X62)
| sP2(X61,relation_dom(relation_dom_restriction(X59,X60)),X62) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_492])]) ).
fof(f1761,plain,
( ! [X59,X62,X60,X61] :
( apply(relation_dom_restriction(X59,X60),sK13(X61,relation_dom(relation_dom_restriction(X59,X60)),X62)) = apply(X59,sK13(X61,relation_dom(relation_dom_restriction(X59,X60)),X62))
| ~ function(X59)
| ~ relation(X59)
| ~ function(relation_dom_restriction(X59,X60))
| ~ relation(relation_dom_restriction(X59,X60))
| in(sK13(X61,relation_dom(relation_dom_restriction(X59,X60)),X62),X62)
| sP2(X61,relation_dom(relation_dom_restriction(X59,X60)),X62) )
| ~ spl22_77
| ~ spl22_185 ),
inference(resolution,[],[f1742,f689]) ).
fof(f6695,plain,
( spl22_491
| ~ spl22_166
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1759,f1741,f1533,f6693]) ).
fof(f6693,plain,
( spl22_491
<=> ! [X51,X54,X53,X52] :
( apply(relation_dom_restriction(X51,X52),sK13(X53,relation_dom(relation_dom_restriction(X51,X52)),X54)) = apply(X51,sK13(X53,relation_dom(relation_dom_restriction(X51,X52)),X54))
| ~ function(X51)
| ~ relation(X51)
| ~ function(relation_dom_restriction(X51,X52))
| ~ relation(relation_dom_restriction(X51,X52))
| element(sK13(X53,relation_dom(relation_dom_restriction(X51,X52)),X54),X54)
| sP2(X53,relation_dom(relation_dom_restriction(X51,X52)),X54) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_491])]) ).
fof(f1759,plain,
( ! [X51,X54,X52,X53] :
( apply(relation_dom_restriction(X51,X52),sK13(X53,relation_dom(relation_dom_restriction(X51,X52)),X54)) = apply(X51,sK13(X53,relation_dom(relation_dom_restriction(X51,X52)),X54))
| ~ function(X51)
| ~ relation(X51)
| ~ function(relation_dom_restriction(X51,X52))
| ~ relation(relation_dom_restriction(X51,X52))
| element(sK13(X53,relation_dom(relation_dom_restriction(X51,X52)),X54),X54)
| sP2(X53,relation_dom(relation_dom_restriction(X51,X52)),X54) )
| ~ spl22_166
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1534]) ).
fof(f6691,plain,
( spl22_490
| ~ spl22_77
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1758,f1741,f688,f6689]) ).
fof(f6689,plain,
( spl22_490
<=> ! [X48,X47,X50,X49] :
( apply(relation_dom_restriction(X47,X48),sK13(X49,X50,relation_dom(relation_dom_restriction(X47,X48)))) = apply(X47,sK13(X49,X50,relation_dom(relation_dom_restriction(X47,X48))))
| ~ function(X47)
| ~ relation(X47)
| ~ function(relation_dom_restriction(X47,X48))
| ~ relation(relation_dom_restriction(X47,X48))
| in(sK13(X49,X50,relation_dom(relation_dom_restriction(X47,X48))),X50)
| sP2(X49,X50,relation_dom(relation_dom_restriction(X47,X48))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_490])]) ).
fof(f1758,plain,
( ! [X50,X48,X49,X47] :
( apply(relation_dom_restriction(X47,X48),sK13(X49,X50,relation_dom(relation_dom_restriction(X47,X48)))) = apply(X47,sK13(X49,X50,relation_dom(relation_dom_restriction(X47,X48))))
| ~ function(X47)
| ~ relation(X47)
| ~ function(relation_dom_restriction(X47,X48))
| ~ relation(relation_dom_restriction(X47,X48))
| in(sK13(X49,X50,relation_dom(relation_dom_restriction(X47,X48))),X50)
| sP2(X49,X50,relation_dom(relation_dom_restriction(X47,X48))) )
| ~ spl22_77
| ~ spl22_185 ),
inference(resolution,[],[f1742,f689]) ).
fof(f6687,plain,
( spl22_489
| ~ spl22_78
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1757,f1741,f692,f6685]) ).
fof(f6685,plain,
( spl22_489
<=> ! [X44,X43,X46,X45] :
( apply(relation_dom_restriction(X43,X44),sK13(X45,X46,relation_dom(relation_dom_restriction(X43,X44)))) = apply(X43,sK13(X45,X46,relation_dom(relation_dom_restriction(X43,X44))))
| ~ function(X43)
| ~ relation(X43)
| ~ function(relation_dom_restriction(X43,X44))
| ~ relation(relation_dom_restriction(X43,X44))
| in(sK13(X45,X46,relation_dom(relation_dom_restriction(X43,X44))),X45)
| sP2(X45,X46,relation_dom(relation_dom_restriction(X43,X44))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_489])]) ).
fof(f1757,plain,
( ! [X46,X44,X45,X43] :
( apply(relation_dom_restriction(X43,X44),sK13(X45,X46,relation_dom(relation_dom_restriction(X43,X44)))) = apply(X43,sK13(X45,X46,relation_dom(relation_dom_restriction(X43,X44))))
| ~ function(X43)
| ~ relation(X43)
| ~ function(relation_dom_restriction(X43,X44))
| ~ relation(relation_dom_restriction(X43,X44))
| in(sK13(X45,X46,relation_dom(relation_dom_restriction(X43,X44))),X45)
| sP2(X45,X46,relation_dom(relation_dom_restriction(X43,X44))) )
| ~ spl22_78
| ~ spl22_185 ),
inference(resolution,[],[f1742,f693]) ).
fof(f6683,plain,
( spl22_488
| ~ spl22_168
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1754,f1741,f1542,f6681]) ).
fof(f6681,plain,
( spl22_488
<=> ! [X31,X34,X33,X32] :
( apply(relation_dom_restriction(X31,X32),sK13(X33,X34,relation_dom(relation_dom_restriction(X31,X32)))) = apply(X31,sK13(X33,X34,relation_dom(relation_dom_restriction(X31,X32))))
| ~ function(X31)
| ~ relation(X31)
| ~ function(relation_dom_restriction(X31,X32))
| ~ relation(relation_dom_restriction(X31,X32))
| element(sK13(X33,X34,relation_dom(relation_dom_restriction(X31,X32))),X34)
| sP2(X33,X34,relation_dom(relation_dom_restriction(X31,X32))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_488])]) ).
fof(f1754,plain,
( ! [X31,X34,X32,X33] :
( apply(relation_dom_restriction(X31,X32),sK13(X33,X34,relation_dom(relation_dom_restriction(X31,X32)))) = apply(X31,sK13(X33,X34,relation_dom(relation_dom_restriction(X31,X32))))
| ~ function(X31)
| ~ relation(X31)
| ~ function(relation_dom_restriction(X31,X32))
| ~ relation(relation_dom_restriction(X31,X32))
| element(sK13(X33,X34,relation_dom(relation_dom_restriction(X31,X32))),X34)
| sP2(X33,X34,relation_dom(relation_dom_restriction(X31,X32))) )
| ~ spl22_168
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1543]) ).
fof(f6679,plain,
( spl22_487
| ~ spl22_172
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1753,f1741,f1558,f6677]) ).
fof(f6677,plain,
( spl22_487
<=> ! [X29,X27,X28,X30] :
( apply(relation_dom_restriction(X27,X28),sK13(X29,X30,relation_dom(relation_dom_restriction(X27,X28)))) = apply(X27,sK13(X29,X30,relation_dom(relation_dom_restriction(X27,X28))))
| ~ function(X27)
| ~ relation(X27)
| ~ function(relation_dom_restriction(X27,X28))
| ~ relation(relation_dom_restriction(X27,X28))
| element(sK13(X29,X30,relation_dom(relation_dom_restriction(X27,X28))),X29)
| sP2(X29,X30,relation_dom(relation_dom_restriction(X27,X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_487])]) ).
fof(f1753,plain,
( ! [X28,X29,X27,X30] :
( apply(relation_dom_restriction(X27,X28),sK13(X29,X30,relation_dom(relation_dom_restriction(X27,X28)))) = apply(X27,sK13(X29,X30,relation_dom(relation_dom_restriction(X27,X28))))
| ~ function(X27)
| ~ relation(X27)
| ~ function(relation_dom_restriction(X27,X28))
| ~ relation(relation_dom_restriction(X27,X28))
| element(sK13(X29,X30,relation_dom(relation_dom_restriction(X27,X28))),X29)
| sP2(X29,X30,relation_dom(relation_dom_restriction(X27,X28))) )
| ~ spl22_172
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1559]) ).
fof(f6657,plain,
( spl22_486
| ~ spl22_74
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1748,f1741,f668,f6655]) ).
fof(f6655,plain,
( spl22_486
<=> ! [X13,X14,X15] :
( apply(relation_dom_restriction(X13,X14),sK7(X15,relation_dom(relation_dom_restriction(X13,X14)))) = apply(X13,sK7(X15,relation_dom(relation_dom_restriction(X13,X14))))
| ~ function(X13)
| ~ relation(X13)
| ~ function(relation_dom_restriction(X13,X14))
| ~ relation(relation_dom_restriction(X13,X14))
| in(sK8(X15,relation_dom(relation_dom_restriction(X13,X14))),relation_dom(X15))
| sP0(X15,relation_dom(relation_dom_restriction(X13,X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_486])]) ).
fof(f1748,plain,
( ! [X14,X15,X13] :
( apply(relation_dom_restriction(X13,X14),sK7(X15,relation_dom(relation_dom_restriction(X13,X14)))) = apply(X13,sK7(X15,relation_dom(relation_dom_restriction(X13,X14))))
| ~ function(X13)
| ~ relation(X13)
| ~ function(relation_dom_restriction(X13,X14))
| ~ relation(relation_dom_restriction(X13,X14))
| in(sK8(X15,relation_dom(relation_dom_restriction(X13,X14))),relation_dom(X15))
| sP0(X15,relation_dom(relation_dom_restriction(X13,X14))) )
| ~ spl22_74
| ~ spl22_185 ),
inference(resolution,[],[f1742,f669]) ).
fof(f6653,plain,
( spl22_485
| ~ spl22_159
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1745,f1741,f1481,f6651]) ).
fof(f6651,plain,
( spl22_485
<=> ! [X6,X4,X5] :
( apply(relation_dom_restriction(X4,X5),sK7(X6,relation_dom(relation_dom_restriction(X4,X5)))) = apply(X4,sK7(X6,relation_dom(relation_dom_restriction(X4,X5))))
| ~ function(X4)
| ~ relation(X4)
| ~ function(relation_dom_restriction(X4,X5))
| ~ relation(relation_dom_restriction(X4,X5))
| element(sK8(X6,relation_dom(relation_dom_restriction(X4,X5))),relation_dom(X6))
| sP0(X6,relation_dom(relation_dom_restriction(X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_485])]) ).
fof(f1745,plain,
( ! [X6,X4,X5] :
( apply(relation_dom_restriction(X4,X5),sK7(X6,relation_dom(relation_dom_restriction(X4,X5)))) = apply(X4,sK7(X6,relation_dom(relation_dom_restriction(X4,X5))))
| ~ function(X4)
| ~ relation(X4)
| ~ function(relation_dom_restriction(X4,X5))
| ~ relation(relation_dom_restriction(X4,X5))
| element(sK8(X6,relation_dom(relation_dom_restriction(X4,X5))),relation_dom(X6))
| sP0(X6,relation_dom(relation_dom_restriction(X4,X5))) )
| ~ spl22_159
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1482]) ).
fof(f6629,plain,
( spl22_484
| ~ spl22_156
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1763,f1741,f1407,f6627]) ).
fof(f6627,plain,
( spl22_484
<=> ! [X69,X70,X67,X68] :
( apply(relation_dom_restriction(X67,X68),sK13(relation_dom(relation_dom_restriction(X67,X68)),X69,X70)) = apply(X67,sK13(relation_dom(relation_dom_restriction(X67,X68)),X69,X70))
| ~ function(X67)
| ~ relation(X67)
| ~ function(relation_dom_restriction(X67,X68))
| ~ relation(relation_dom_restriction(X67,X68))
| sP2(relation_dom(relation_dom_restriction(X67,X68)),X69,X70)
| ~ empty(X70) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_484])]) ).
fof(f1763,plain,
( ! [X70,X68,X69,X67] :
( apply(relation_dom_restriction(X67,X68),sK13(relation_dom(relation_dom_restriction(X67,X68)),X69,X70)) = apply(X67,sK13(relation_dom(relation_dom_restriction(X67,X68)),X69,X70))
| ~ function(X67)
| ~ relation(X67)
| ~ function(relation_dom_restriction(X67,X68))
| ~ relation(relation_dom_restriction(X67,X68))
| sP2(relation_dom(relation_dom_restriction(X67,X68)),X69,X70)
| ~ empty(X70) )
| ~ spl22_156
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1408]) ).
fof(f6625,plain,
( spl22_483
| ~ spl22_154
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1760,f1741,f1399,f6623]) ).
fof(f6623,plain,
( spl22_483
<=> ! [X55,X57,X56,X58] :
( apply(relation_dom_restriction(X55,X56),sK13(X57,relation_dom(relation_dom_restriction(X55,X56)),X58)) = apply(X55,sK13(X57,relation_dom(relation_dom_restriction(X55,X56)),X58))
| ~ function(X55)
| ~ relation(X55)
| ~ function(relation_dom_restriction(X55,X56))
| ~ relation(relation_dom_restriction(X55,X56))
| sP2(X57,relation_dom(relation_dom_restriction(X55,X56)),X58)
| ~ empty(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_483])]) ).
fof(f1760,plain,
( ! [X58,X56,X57,X55] :
( apply(relation_dom_restriction(X55,X56),sK13(X57,relation_dom(relation_dom_restriction(X55,X56)),X58)) = apply(X55,sK13(X57,relation_dom(relation_dom_restriction(X55,X56)),X58))
| ~ function(X55)
| ~ relation(X55)
| ~ function(relation_dom_restriction(X55,X56))
| ~ relation(relation_dom_restriction(X55,X56))
| sP2(X57,relation_dom(relation_dom_restriction(X55,X56)),X58)
| ~ empty(X58) )
| ~ spl22_154
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1400]) ).
fof(f6621,plain,
( spl22_482
| ~ spl22_155
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1756,f1741,f1403,f6619]) ).
fof(f6619,plain,
( spl22_482
<=> ! [X41,X40,X42,X39] :
( apply(relation_dom_restriction(X39,X40),sK13(X41,X42,relation_dom(relation_dom_restriction(X39,X40)))) = apply(X39,sK13(X41,X42,relation_dom(relation_dom_restriction(X39,X40))))
| ~ function(X39)
| ~ relation(X39)
| ~ function(relation_dom_restriction(X39,X40))
| ~ relation(relation_dom_restriction(X39,X40))
| sP2(X41,X42,relation_dom(relation_dom_restriction(X39,X40)))
| ~ empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_482])]) ).
fof(f1756,plain,
( ! [X40,X41,X39,X42] :
( apply(relation_dom_restriction(X39,X40),sK13(X41,X42,relation_dom(relation_dom_restriction(X39,X40)))) = apply(X39,sK13(X41,X42,relation_dom(relation_dom_restriction(X39,X40))))
| ~ function(X39)
| ~ relation(X39)
| ~ function(relation_dom_restriction(X39,X40))
| ~ relation(relation_dom_restriction(X39,X40))
| sP2(X41,X42,relation_dom(relation_dom_restriction(X39,X40)))
| ~ empty(X42) )
| ~ spl22_155
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1404]) ).
fof(f6617,plain,
( spl22_481
| ~ spl22_157
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1755,f1741,f1411,f6615]) ).
fof(f6615,plain,
( spl22_481
<=> ! [X38,X36,X35,X37] :
( apply(relation_dom_restriction(X35,X36),sK13(X37,X38,relation_dom(relation_dom_restriction(X35,X36)))) = apply(X35,sK13(X37,X38,relation_dom(relation_dom_restriction(X35,X36))))
| ~ function(X35)
| ~ relation(X35)
| ~ function(relation_dom_restriction(X35,X36))
| ~ relation(relation_dom_restriction(X35,X36))
| sP2(X37,X38,relation_dom(relation_dom_restriction(X35,X36)))
| ~ empty(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_481])]) ).
fof(f1755,plain,
( ! [X38,X36,X37,X35] :
( apply(relation_dom_restriction(X35,X36),sK13(X37,X38,relation_dom(relation_dom_restriction(X35,X36)))) = apply(X35,sK13(X37,X38,relation_dom(relation_dom_restriction(X35,X36))))
| ~ function(X35)
| ~ relation(X35)
| ~ function(relation_dom_restriction(X35,X36))
| ~ relation(relation_dom_restriction(X35,X36))
| sP2(X37,X38,relation_dom(relation_dom_restriction(X35,X36)))
| ~ empty(X37) )
| ~ spl22_157
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1412]) ).
fof(f6578,plain,
( spl22_480
| ~ spl22_74
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1751,f1741,f668,f6576]) ).
fof(f6576,plain,
( spl22_480
<=> ! [X22,X24,X23] :
( apply(relation_dom_restriction(X22,X23),sK8(relation_dom_restriction(X22,X23),X24)) = apply(X22,sK8(relation_dom_restriction(X22,X23),X24))
| ~ function(X22)
| ~ relation(X22)
| ~ function(relation_dom_restriction(X22,X23))
| ~ relation(relation_dom_restriction(X22,X23))
| in(sK7(relation_dom_restriction(X22,X23),X24),X24)
| sP0(relation_dom_restriction(X22,X23),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_480])]) ).
fof(f1751,plain,
( ! [X24,X22,X23] :
( apply(relation_dom_restriction(X22,X23),sK8(relation_dom_restriction(X22,X23),X24)) = apply(X22,sK8(relation_dom_restriction(X22,X23),X24))
| ~ function(X22)
| ~ relation(X22)
| ~ function(relation_dom_restriction(X22,X23))
| ~ relation(relation_dom_restriction(X22,X23))
| in(sK7(relation_dom_restriction(X22,X23),X24),X24)
| sP0(relation_dom_restriction(X22,X23),X24) )
| ~ spl22_74
| ~ spl22_185 ),
inference(resolution,[],[f1742,f669]) ).
fof(f6574,plain,
( spl22_479
| ~ spl22_161
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1749,f1741,f1489,f6572]) ).
fof(f6572,plain,
( spl22_479
<=> ! [X18,X16,X17] :
( apply(relation_dom_restriction(X16,X17),sK8(relation_dom_restriction(X16,X17),X18)) = apply(X16,sK8(relation_dom_restriction(X16,X17),X18))
| ~ function(X16)
| ~ relation(X16)
| ~ function(relation_dom_restriction(X16,X17))
| ~ relation(relation_dom_restriction(X16,X17))
| element(sK7(relation_dom_restriction(X16,X17),X18),X18)
| sP0(relation_dom_restriction(X16,X17),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_479])]) ).
fof(f1749,plain,
( ! [X18,X16,X17] :
( apply(relation_dom_restriction(X16,X17),sK8(relation_dom_restriction(X16,X17),X18)) = apply(X16,sK8(relation_dom_restriction(X16,X17),X18))
| ~ function(X16)
| ~ relation(X16)
| ~ function(relation_dom_restriction(X16,X17))
| ~ relation(relation_dom_restriction(X16,X17))
| element(sK7(relation_dom_restriction(X16,X17),X18),X18)
| sP0(relation_dom_restriction(X16,X17),X18) )
| ~ spl22_161
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1490]) ).
fof(f6561,plain,
( spl22_478
| ~ spl22_149
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1746,f1741,f1362,f6559]) ).
fof(f6559,plain,
( spl22_478
<=> ! [X9,X8,X7] :
( apply(relation_dom_restriction(X7,X8),sK7(X9,relation_dom(relation_dom_restriction(X7,X8)))) = apply(X7,sK7(X9,relation_dom(relation_dom_restriction(X7,X8))))
| ~ function(X7)
| ~ relation(X7)
| ~ function(relation_dom_restriction(X7,X8))
| ~ relation(relation_dom_restriction(X7,X8))
| sP0(X9,relation_dom(relation_dom_restriction(X7,X8)))
| ~ empty(relation_dom(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_478])]) ).
fof(f1746,plain,
( ! [X8,X9,X7] :
( apply(relation_dom_restriction(X7,X8),sK7(X9,relation_dom(relation_dom_restriction(X7,X8)))) = apply(X7,sK7(X9,relation_dom(relation_dom_restriction(X7,X8))))
| ~ function(X7)
| ~ relation(X7)
| ~ function(relation_dom_restriction(X7,X8))
| ~ relation(relation_dom_restriction(X7,X8))
| sP0(X9,relation_dom(relation_dom_restriction(X7,X8)))
| ~ empty(relation_dom(X9)) )
| ~ spl22_149
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1363]) ).
fof(f6543,plain,
( spl22_476
| ~ spl22_477
| ~ spl22_214
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4512,f3672,f2112,f6540,f6536]) ).
fof(f6540,plain,
( spl22_477
<=> sP0(sK5,sK10(sK7(sK5,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_477])]) ).
fof(f4512,plain,
( ~ sP0(sK5,sK10(sK7(sK5,sK15)))
| empty(sK7(sK5,sK15))
| ~ spl22_214
| ~ spl22_340 ),
inference(resolution,[],[f3673,f2113]) ).
fof(f6513,plain,
( spl22_475
| ~ spl22_59
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1867,f1784,f552,f6511]) ).
fof(f6511,plain,
( spl22_475
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(set_intersection2(X2,X3),X1),sK7(X0,X1)) = apply(set_intersection2(X2,X3),sK7(X0,X1))
| ~ function(set_intersection2(X2,X3))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ relation(X3)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_475])]) ).
fof(f1784,plain,
( spl22_190
<=> ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_190])]) ).
fof(f1867,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1)
| apply(relation_dom_restriction(set_intersection2(X2,X3),X1),sK7(X0,X1)) = apply(set_intersection2(X2,X3),sK7(X0,X1))
| ~ function(set_intersection2(X2,X3))
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| ~ relation(X3)
| ~ relation(X2) )
| ~ spl22_59
| ~ spl22_190 ),
inference(resolution,[],[f1785,f553]) ).
fof(f1785,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| sK7(X0,X1) = apply(X0,sK8(X0,X1)) )
| ~ spl22_190 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f6509,plain,
( spl22_474
| ~ spl22_59
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1848,f1780,f552,f6507]) ).
fof(f6507,plain,
( spl22_474
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X0),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_474])]) ).
fof(f1780,plain,
( spl22_189
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_189])]) ).
fof(f1848,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X0),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_189 ),
inference(resolution,[],[f1781,f553]) ).
fof(f1781,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_189 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f6505,plain,
( spl22_473
| ~ spl22_59
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1829,f1776,f552,f6503]) ).
fof(f6503,plain,
( spl22_473
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X0)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_473])]) ).
fof(f1776,plain,
( spl22_188
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_188])]) ).
fof(f1829,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X0)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_188 ),
inference(resolution,[],[f1777,f553]) ).
fof(f1777,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X0) )
| ~ spl22_188 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f6501,plain,
( spl22_472
| ~ spl22_59
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1810,f1772,f552,f6499]) ).
fof(f6499,plain,
( spl22_472
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X1),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_472])]) ).
fof(f1772,plain,
( spl22_187
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_187])]) ).
fof(f1810,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(set_intersection2(X3,X4),sK13(X0,X1,X2)) = apply(relation_dom_restriction(set_intersection2(X3,X4),X1),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X2)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_187 ),
inference(resolution,[],[f1773,f553]) ).
fof(f1773,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X2) )
| ~ spl22_187 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f6497,plain,
( spl22_471
| ~ spl22_59
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1791,f1768,f552,f6495]) ).
fof(f6495,plain,
( spl22_471
<=> ! [X4,X0,X3,X2,X1] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X1)
| ~ relation(X4)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_471])]) ).
fof(f1768,plain,
( spl22_186
<=> ! [X0,X3,X2,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_186])]) ).
fof(f1791,plain,
( ! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| apply(relation_dom_restriction(set_intersection2(X3,X4),X2),sK13(X0,X1,X2)) = apply(set_intersection2(X3,X4),sK13(X0,X1,X2))
| ~ function(set_intersection2(X3,X4))
| in(sK13(X0,X1,X2),X1)
| ~ relation(X4)
| ~ relation(X3) )
| ~ spl22_59
| ~ spl22_186 ),
inference(resolution,[],[f1769,f553]) ).
fof(f1769,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X3)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| in(sK13(X0,X1,X2),X1) )
| ~ spl22_186 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f6480,plain,
( spl22_470
| ~ spl22_150
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1750,f1741,f1366,f6478]) ).
fof(f6478,plain,
( spl22_470
<=> ! [X20,X21,X19] :
( apply(relation_dom_restriction(X19,X20),sK8(relation_dom_restriction(X19,X20),X21)) = apply(X19,sK8(relation_dom_restriction(X19,X20),X21))
| ~ function(X19)
| ~ relation(X19)
| ~ function(relation_dom_restriction(X19,X20))
| ~ relation(relation_dom_restriction(X19,X20))
| sP0(relation_dom_restriction(X19,X20),X21)
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_470])]) ).
fof(f1750,plain,
( ! [X21,X19,X20] :
( apply(relation_dom_restriction(X19,X20),sK8(relation_dom_restriction(X19,X20),X21)) = apply(X19,sK8(relation_dom_restriction(X19,X20),X21))
| ~ function(X19)
| ~ relation(X19)
| ~ function(relation_dom_restriction(X19,X20))
| ~ relation(relation_dom_restriction(X19,X20))
| sP0(relation_dom_restriction(X19,X20),X21)
| ~ empty(X21) )
| ~ spl22_150
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1367]) ).
fof(f6476,plain,
( spl22_469
| ~ spl22_137
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4510,f3672,f1213,f6474]) ).
fof(f6474,plain,
( spl22_469
<=> ! [X26] :
( ~ sP0(sK5,sK10(powerset(X26)))
| element(sK7(sK5,sK15),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_469])]) ).
fof(f4510,plain,
( ! [X26] :
( ~ sP0(sK5,sK10(powerset(X26)))
| element(sK7(sK5,sK15),X26) )
| ~ spl22_137
| ~ spl22_340 ),
inference(resolution,[],[f3673,f1214]) ).
fof(f6451,plain,
( spl22_468
| ~ spl22_44
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1870,f1784,f444,f6449]) ).
fof(f6449,plain,
( spl22_468
<=> ! [X10,X11,X13,X12] :
( sP0(X10,X11)
| apply(relation_dom_restriction(relation_dom_restriction(X12,X13),X11),sK7(X10,X11)) = apply(relation_dom_restriction(X12,X13),sK7(X10,X11))
| ~ function(relation_dom_restriction(X12,X13))
| sK7(X10,X11) = apply(X10,sK8(X10,X11))
| ~ relation(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_468])]) ).
fof(f1870,plain,
( ! [X10,X11,X12,X13] :
( sP0(X10,X11)
| apply(relation_dom_restriction(relation_dom_restriction(X12,X13),X11),sK7(X10,X11)) = apply(relation_dom_restriction(X12,X13),sK7(X10,X11))
| ~ function(relation_dom_restriction(X12,X13))
| sK7(X10,X11) = apply(X10,sK8(X10,X11))
| ~ relation(X12) )
| ~ spl22_44
| ~ spl22_190 ),
inference(resolution,[],[f1785,f445]) ).
fof(f6447,plain,
( spl22_467
| ~ spl22_44
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1851,f1780,f444,f6445]) ).
fof(f6445,plain,
( spl22_467
<=> ! [X17,X13,X14,X16,X15] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15)) = apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X13),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X15)
| ~ relation(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_467])]) ).
fof(f1851,plain,
( ! [X16,X14,X17,X15,X13] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15)) = apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X13),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X15)
| ~ relation(X16) )
| ~ spl22_44
| ~ spl22_189 ),
inference(resolution,[],[f1781,f445]) ).
fof(f6443,plain,
( spl22_466
| ~ spl22_44
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1832,f1776,f444,f6441]) ).
fof(f6441,plain,
( spl22_466
<=> ! [X17,X13,X14,X16,X15] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X15),sK13(X13,X14,X15)) = apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X13)
| ~ relation(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_466])]) ).
fof(f1832,plain,
( ! [X16,X14,X17,X15,X13] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X15),sK13(X13,X14,X15)) = apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X13)
| ~ relation(X16) )
| ~ spl22_44
| ~ spl22_188 ),
inference(resolution,[],[f1777,f445]) ).
fof(f6439,plain,
( spl22_465
| ~ spl22_44
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1813,f1772,f444,f6437]) ).
fof(f6437,plain,
( spl22_465
<=> ! [X17,X13,X14,X16,X15] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15)) = apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X14),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X15)
| ~ relation(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_465])]) ).
fof(f1813,plain,
( ! [X16,X14,X17,X15,X13] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15)) = apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X14),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X15)
| ~ relation(X16) )
| ~ spl22_44
| ~ spl22_187 ),
inference(resolution,[],[f1773,f445]) ).
fof(f6435,plain,
( spl22_464
| ~ spl22_237
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4497,f3672,f2435,f6433]) ).
fof(f6433,plain,
( spl22_464
<=> ! [X8,X7] :
( ~ sP0(sK5,set_intersection2(X7,X8))
| in(sK7(sK5,sK15),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_464])]) ).
fof(f4497,plain,
( ! [X8,X7] :
( ~ sP0(sK5,set_intersection2(X7,X8))
| in(sK7(sK5,sK15),X8) )
| ~ spl22_237
| ~ spl22_340 ),
inference(resolution,[],[f3673,f2436]) ).
fof(f6431,plain,
( spl22_463
| ~ spl22_44
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1794,f1768,f444,f6429]) ).
fof(f6429,plain,
( spl22_463
<=> ! [X17,X13,X14,X16,X15] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X15),sK13(X13,X14,X15)) = apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X14)
| ~ relation(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_463])]) ).
fof(f1794,plain,
( ! [X16,X14,X17,X15,X13] :
( sP2(X13,X14,X15)
| apply(relation_dom_restriction(relation_dom_restriction(X16,X17),X15),sK13(X13,X14,X15)) = apply(relation_dom_restriction(X16,X17),sK13(X13,X14,X15))
| ~ function(relation_dom_restriction(X16,X17))
| in(sK13(X13,X14,X15),X14)
| ~ relation(X16) )
| ~ spl22_44
| ~ spl22_186 ),
inference(resolution,[],[f1769,f445]) ).
fof(f6427,plain,
( spl22_462
| ~ spl22_153
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1744,f1741,f1395,f6425]) ).
fof(f1744,plain,
( ! [X2,X3,X0,X1] :
( apply(relation_dom_restriction(X0,X1),apply(X2,X3)) = apply(X0,apply(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,relation_dom(relation_dom_restriction(X0,X1))) )
| ~ spl22_153
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1396]) ).
fof(f6380,plain,
( spl22_461
| ~ spl22_124
| ~ spl22_185 ),
inference(avatar_split_clause,[],[f1752,f1741,f1103,f6378]) ).
fof(f6378,plain,
( spl22_461
<=> ! [X25,X26] :
( apply(relation_dom_restriction(X25,X26),sK10(relation_dom(relation_dom_restriction(X25,X26)))) = apply(X25,sK10(relation_dom(relation_dom_restriction(X25,X26))))
| ~ function(X25)
| ~ relation(X25)
| ~ function(relation_dom_restriction(X25,X26))
| ~ relation(relation_dom_restriction(X25,X26))
| empty(relation_dom(relation_dom_restriction(X25,X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_461])]) ).
fof(f1752,plain,
( ! [X26,X25] :
( apply(relation_dom_restriction(X25,X26),sK10(relation_dom(relation_dom_restriction(X25,X26)))) = apply(X25,sK10(relation_dom(relation_dom_restriction(X25,X26))))
| ~ function(X25)
| ~ relation(X25)
| ~ function(relation_dom_restriction(X25,X26))
| ~ relation(relation_dom_restriction(X25,X26))
| empty(relation_dom(relation_dom_restriction(X25,X26))) )
| ~ spl22_124
| ~ spl22_185 ),
inference(resolution,[],[f1742,f1104]) ).
fof(f6376,plain,
( spl22_460
| ~ spl22_59
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1716,f1685,f552,f6374]) ).
fof(f6374,plain,
( spl22_460
<=> ! [X0,X3,X2,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),X2),sK7(X3,X2)) = apply(set_intersection2(X0,X1),sK7(X3,X2))
| in(sK8(X3,X2),relation_dom(X3))
| sP0(X3,X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_460])]) ).
fof(f1685,plain,
( spl22_182
<=> ! [X6,X5,X7] :
( apply(relation_dom_restriction(X5,X6),sK7(X7,X6)) = apply(X5,sK7(X7,X6))
| ~ function(X5)
| ~ relation(X5)
| in(sK8(X7,X6),relation_dom(X7))
| sP0(X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_182])]) ).
fof(f1716,plain,
( ! [X2,X3,X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),X2),sK7(X3,X2)) = apply(set_intersection2(X0,X1),sK7(X3,X2))
| in(sK8(X3,X2),relation_dom(X3))
| sP0(X3,X2)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_182 ),
inference(resolution,[],[f1686,f553]) ).
fof(f1686,plain,
( ! [X6,X7,X5] :
( ~ relation(X5)
| ~ function(X5)
| apply(relation_dom_restriction(X5,X6),sK7(X7,X6)) = apply(X5,sK7(X7,X6))
| in(sK8(X7,X6),relation_dom(X7))
| sP0(X7,X6) )
| ~ spl22_182 ),
inference(avatar_component_clause,[],[f1685]) ).
fof(f6372,plain,
( spl22_459
| ~ spl22_59
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1697,f1681,f552,f6370]) ).
fof(f6370,plain,
( spl22_459
<=> ! [X0,X3,X2,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(X2)),sK8(X2,X3)) = apply(set_intersection2(X0,X1),sK8(X2,X3))
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_459])]) ).
fof(f1681,plain,
( spl22_181
<=> ! [X4,X2,X3] :
( apply(relation_dom_restriction(X2,relation_dom(X3)),sK8(X3,X4)) = apply(X2,sK8(X3,X4))
| ~ function(X2)
| ~ relation(X2)
| in(sK7(X3,X4),X4)
| sP0(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_181])]) ).
fof(f1697,plain,
( ! [X2,X3,X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(X2)),sK8(X2,X3)) = apply(set_intersection2(X0,X1),sK8(X2,X3))
| in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_181 ),
inference(resolution,[],[f1682,f553]) ).
fof(f1682,plain,
( ! [X2,X3,X4] :
( ~ relation(X2)
| ~ function(X2)
| apply(relation_dom_restriction(X2,relation_dom(X3)),sK8(X3,X4)) = apply(X2,sK8(X3,X4))
| in(sK7(X3,X4),X4)
| sP0(X3,X4) )
| ~ spl22_181 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f6362,plain,
( spl22_458
| ~ spl22_238
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4496,f3672,f2439,f6360]) ).
fof(f6360,plain,
( spl22_458
<=> ! [X6,X5] :
( ~ sP0(sK5,set_intersection2(X5,X6))
| in(sK7(sK5,sK15),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_458])]) ).
fof(f4496,plain,
( ! [X6,X5] :
( ~ sP0(sK5,set_intersection2(X5,X6))
| in(sK7(sK5,sK15),X5) )
| ~ spl22_238
| ~ spl22_340 ),
inference(resolution,[],[f3673,f2440]) ).
fof(f6325,plain,
( spl22_457
| ~ spl22_37
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1869,f1784,f397,f6323]) ).
fof(f6323,plain,
( spl22_457
<=> ! [X9,X8,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(relation_dom(X9),X8),sK7(X7,X8)) = apply(relation_dom(X9),sK7(X7,X8))
| ~ function(relation_dom(X9))
| sK7(X7,X8) = apply(X7,sK8(X7,X8))
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_457])]) ).
fof(f1869,plain,
( ! [X8,X9,X7] :
( sP0(X7,X8)
| apply(relation_dom_restriction(relation_dom(X9),X8),sK7(X7,X8)) = apply(relation_dom(X9),sK7(X7,X8))
| ~ function(relation_dom(X9))
| sK7(X7,X8) = apply(X7,sK8(X7,X8))
| ~ empty(X9) )
| ~ spl22_37
| ~ spl22_190 ),
inference(resolution,[],[f1785,f398]) ).
fof(f6321,plain,
( spl22_456
| ~ spl22_35
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1868,f1784,f389,f6319]) ).
fof(f6319,plain,
( spl22_456
<=> ! [X6,X4,X5] :
( sP0(X4,X5)
| apply(relation_dom_restriction(relation_rng(X6),X5),sK7(X4,X5)) = apply(relation_rng(X6),sK7(X4,X5))
| ~ function(relation_rng(X6))
| sK7(X4,X5) = apply(X4,sK8(X4,X5))
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_456])]) ).
fof(f1868,plain,
( ! [X6,X4,X5] :
( sP0(X4,X5)
| apply(relation_dom_restriction(relation_rng(X6),X5),sK7(X4,X5)) = apply(relation_rng(X6),sK7(X4,X5))
| ~ function(relation_rng(X6))
| sK7(X4,X5) = apply(X4,sK8(X4,X5))
| ~ empty(X6) )
| ~ spl22_35
| ~ spl22_190 ),
inference(resolution,[],[f1785,f390]) ).
fof(f6317,plain,
( spl22_455
| ~ spl22_37
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1850,f1780,f397,f6315]) ).
fof(f6315,plain,
( spl22_455
<=> ! [X10,X11,X12,X9] :
( sP2(X9,X10,X11)
| apply(relation_dom(X12),sK13(X9,X10,X11)) = apply(relation_dom_restriction(relation_dom(X12),X9),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X11)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_455])]) ).
fof(f1850,plain,
( ! [X10,X11,X9,X12] :
( sP2(X9,X10,X11)
| apply(relation_dom(X12),sK13(X9,X10,X11)) = apply(relation_dom_restriction(relation_dom(X12),X9),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X11)
| ~ empty(X12) )
| ~ spl22_37
| ~ spl22_189 ),
inference(resolution,[],[f1781,f398]) ).
fof(f6313,plain,
( spl22_454
| ~ spl22_35
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1849,f1780,f389,f6311]) ).
fof(f6311,plain,
( spl22_454
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| apply(relation_rng(X8),sK13(X5,X6,X7)) = apply(relation_dom_restriction(relation_rng(X8),X5),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X7)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_454])]) ).
fof(f1849,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| apply(relation_rng(X8),sK13(X5,X6,X7)) = apply(relation_dom_restriction(relation_rng(X8),X5),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X7)
| ~ empty(X8) )
| ~ spl22_35
| ~ spl22_189 ),
inference(resolution,[],[f1781,f390]) ).
fof(f6309,plain,
( spl22_453
| ~ spl22_37
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1831,f1776,f397,f6307]) ).
fof(f6307,plain,
( spl22_453
<=> ! [X10,X11,X12,X9] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(relation_dom(X12),X11),sK13(X9,X10,X11)) = apply(relation_dom(X12),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X9)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_453])]) ).
fof(f1831,plain,
( ! [X10,X11,X9,X12] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(relation_dom(X12),X11),sK13(X9,X10,X11)) = apply(relation_dom(X12),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X9)
| ~ empty(X12) )
| ~ spl22_37
| ~ spl22_188 ),
inference(resolution,[],[f1777,f398]) ).
fof(f6305,plain,
( spl22_452
| ~ spl22_35
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1830,f1776,f389,f6303]) ).
fof(f6303,plain,
( spl22_452
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(relation_rng(X8),X7),sK13(X5,X6,X7)) = apply(relation_rng(X8),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X5)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_452])]) ).
fof(f1830,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(relation_rng(X8),X7),sK13(X5,X6,X7)) = apply(relation_rng(X8),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X5)
| ~ empty(X8) )
| ~ spl22_35
| ~ spl22_188 ),
inference(resolution,[],[f1777,f390]) ).
fof(f6301,plain,
( spl22_451
| ~ spl22_37
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1812,f1772,f397,f6299]) ).
fof(f6299,plain,
( spl22_451
<=> ! [X10,X11,X12,X9] :
( sP2(X9,X10,X11)
| apply(relation_dom(X12),sK13(X9,X10,X11)) = apply(relation_dom_restriction(relation_dom(X12),X10),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X11)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_451])]) ).
fof(f1812,plain,
( ! [X10,X11,X9,X12] :
( sP2(X9,X10,X11)
| apply(relation_dom(X12),sK13(X9,X10,X11)) = apply(relation_dom_restriction(relation_dom(X12),X10),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X11)
| ~ empty(X12) )
| ~ spl22_37
| ~ spl22_187 ),
inference(resolution,[],[f1773,f398]) ).
fof(f6297,plain,
( spl22_450
| ~ spl22_35
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1811,f1772,f389,f6295]) ).
fof(f6295,plain,
( spl22_450
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| apply(relation_rng(X8),sK13(X5,X6,X7)) = apply(relation_dom_restriction(relation_rng(X8),X6),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X7)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_450])]) ).
fof(f1811,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| apply(relation_rng(X8),sK13(X5,X6,X7)) = apply(relation_dom_restriction(relation_rng(X8),X6),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X7)
| ~ empty(X8) )
| ~ spl22_35
| ~ spl22_187 ),
inference(resolution,[],[f1773,f390]) ).
fof(f6293,plain,
( spl22_449
| ~ spl22_37
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1793,f1768,f397,f6291]) ).
fof(f6291,plain,
( spl22_449
<=> ! [X10,X11,X12,X9] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(relation_dom(X12),X11),sK13(X9,X10,X11)) = apply(relation_dom(X12),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X10)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_449])]) ).
fof(f1793,plain,
( ! [X10,X11,X9,X12] :
( sP2(X9,X10,X11)
| apply(relation_dom_restriction(relation_dom(X12),X11),sK13(X9,X10,X11)) = apply(relation_dom(X12),sK13(X9,X10,X11))
| ~ function(relation_dom(X12))
| in(sK13(X9,X10,X11),X10)
| ~ empty(X12) )
| ~ spl22_37
| ~ spl22_186 ),
inference(resolution,[],[f1769,f398]) ).
fof(f6289,plain,
( spl22_448
| ~ spl22_35
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1792,f1768,f389,f6287]) ).
fof(f6287,plain,
( spl22_448
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(relation_rng(X8),X7),sK13(X5,X6,X7)) = apply(relation_rng(X8),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X6)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_448])]) ).
fof(f1792,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| apply(relation_dom_restriction(relation_rng(X8),X7),sK13(X5,X6,X7)) = apply(relation_rng(X8),sK13(X5,X6,X7))
| ~ function(relation_rng(X8))
| in(sK13(X5,X6,X7),X6)
| ~ empty(X8) )
| ~ spl22_35
| ~ spl22_186 ),
inference(resolution,[],[f1769,f390]) ).
fof(f6285,plain,
( spl22_447
| ~ spl22_52
| ~ spl22_404 ),
inference(avatar_split_clause,[],[f5471,f5199,f498,f6283]) ).
fof(f6283,plain,
( spl22_447
<=> ! [X4] :
( ~ sP0(sK5,powerset(X4))
| subset(sK7(sK5,sK15),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_447])]) ).
fof(f5199,plain,
( spl22_404
<=> ! [X3] :
( ~ sP0(sK5,X3)
| element(sK7(sK5,sK15),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_404])]) ).
fof(f5471,plain,
( ! [X4] :
( ~ sP0(sK5,powerset(X4))
| subset(sK7(sK5,sK15),X4) )
| ~ spl22_52
| ~ spl22_404 ),
inference(resolution,[],[f5200,f499]) ).
fof(f5200,plain,
( ! [X3] :
( element(sK7(sK5,sK15),X3)
| ~ sP0(sK5,X3) )
| ~ spl22_404 ),
inference(avatar_component_clause,[],[f5199]) ).
fof(f6281,plain,
( spl22_446
| ~ spl22_44
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1719,f1685,f444,f6279]) ).
fof(f6279,plain,
( spl22_446
<=> ! [X10,X11,X13,X12] :
( ~ function(relation_dom_restriction(X10,X11))
| apply(relation_dom_restriction(relation_dom_restriction(X10,X11),X12),sK7(X13,X12)) = apply(relation_dom_restriction(X10,X11),sK7(X13,X12))
| in(sK8(X13,X12),relation_dom(X13))
| sP0(X13,X12)
| ~ relation(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_446])]) ).
fof(f1719,plain,
( ! [X10,X11,X12,X13] :
( ~ function(relation_dom_restriction(X10,X11))
| apply(relation_dom_restriction(relation_dom_restriction(X10,X11),X12),sK7(X13,X12)) = apply(relation_dom_restriction(X10,X11),sK7(X13,X12))
| in(sK8(X13,X12),relation_dom(X13))
| sP0(X13,X12)
| ~ relation(X10) )
| ~ spl22_44
| ~ spl22_182 ),
inference(resolution,[],[f1686,f445]) ).
fof(f6277,plain,
( spl22_445
| ~ spl22_44
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1700,f1681,f444,f6275]) ).
fof(f6275,plain,
( spl22_445
<=> ! [X10,X11,X13,X12] :
( ~ function(relation_dom_restriction(X10,X11))
| apply(relation_dom_restriction(relation_dom_restriction(X10,X11),relation_dom(X12)),sK8(X12,X13)) = apply(relation_dom_restriction(X10,X11),sK8(X12,X13))
| in(sK7(X12,X13),X13)
| sP0(X12,X13)
| ~ relation(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_445])]) ).
fof(f1700,plain,
( ! [X10,X11,X12,X13] :
( ~ function(relation_dom_restriction(X10,X11))
| apply(relation_dom_restriction(relation_dom_restriction(X10,X11),relation_dom(X12)),sK8(X12,X13)) = apply(relation_dom_restriction(X10,X11),sK8(X12,X13))
| in(sK7(X12,X13),X13)
| sP0(X12,X13)
| ~ relation(X10) )
| ~ spl22_44
| ~ spl22_181 ),
inference(resolution,[],[f1682,f445]) ).
fof(f6169,plain,
( spl22_444
| ~ spl22_37
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1718,f1685,f397,f6167]) ).
fof(f6167,plain,
( spl22_444
<=> ! [X9,X7,X8] :
( ~ function(relation_dom(X7))
| apply(relation_dom_restriction(relation_dom(X7),X8),sK7(X9,X8)) = apply(relation_dom(X7),sK7(X9,X8))
| in(sK8(X9,X8),relation_dom(X9))
| sP0(X9,X8)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_444])]) ).
fof(f1718,plain,
( ! [X8,X9,X7] :
( ~ function(relation_dom(X7))
| apply(relation_dom_restriction(relation_dom(X7),X8),sK7(X9,X8)) = apply(relation_dom(X7),sK7(X9,X8))
| in(sK8(X9,X8),relation_dom(X9))
| sP0(X9,X8)
| ~ empty(X7) )
| ~ spl22_37
| ~ spl22_182 ),
inference(resolution,[],[f1686,f398]) ).
fof(f6165,plain,
( spl22_443
| ~ spl22_35
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1717,f1685,f389,f6163]) ).
fof(f6163,plain,
( spl22_443
<=> ! [X6,X4,X5] :
( ~ function(relation_rng(X4))
| apply(relation_dom_restriction(relation_rng(X4),X5),sK7(X6,X5)) = apply(relation_rng(X4),sK7(X6,X5))
| in(sK8(X6,X5),relation_dom(X6))
| sP0(X6,X5)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_443])]) ).
fof(f1717,plain,
( ! [X6,X4,X5] :
( ~ function(relation_rng(X4))
| apply(relation_dom_restriction(relation_rng(X4),X5),sK7(X6,X5)) = apply(relation_rng(X4),sK7(X6,X5))
| in(sK8(X6,X5),relation_dom(X6))
| sP0(X6,X5)
| ~ empty(X4) )
| ~ spl22_35
| ~ spl22_182 ),
inference(resolution,[],[f1686,f390]) ).
fof(f6161,plain,
( spl22_442
| ~ spl22_37
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1699,f1681,f397,f6159]) ).
fof(f6159,plain,
( spl22_442
<=> ! [X9,X7,X8] :
( ~ function(relation_dom(X7))
| apply(relation_dom_restriction(relation_dom(X7),relation_dom(X8)),sK8(X8,X9)) = apply(relation_dom(X7),sK8(X8,X9))
| in(sK7(X8,X9),X9)
| sP0(X8,X9)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_442])]) ).
fof(f1699,plain,
( ! [X8,X9,X7] :
( ~ function(relation_dom(X7))
| apply(relation_dom_restriction(relation_dom(X7),relation_dom(X8)),sK8(X8,X9)) = apply(relation_dom(X7),sK8(X8,X9))
| in(sK7(X8,X9),X9)
| sP0(X8,X9)
| ~ empty(X7) )
| ~ spl22_37
| ~ spl22_181 ),
inference(resolution,[],[f1682,f398]) ).
fof(f6157,plain,
( spl22_441
| ~ spl22_35
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1698,f1681,f389,f6155]) ).
fof(f6155,plain,
( spl22_441
<=> ! [X6,X4,X5] :
( ~ function(relation_rng(X4))
| apply(relation_dom_restriction(relation_rng(X4),relation_dom(X5)),sK8(X5,X6)) = apply(relation_rng(X4),sK8(X5,X6))
| in(sK7(X5,X6),X6)
| sP0(X5,X6)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_441])]) ).
fof(f1698,plain,
( ! [X6,X4,X5] :
( ~ function(relation_rng(X4))
| apply(relation_dom_restriction(relation_rng(X4),relation_dom(X5)),sK8(X5,X6)) = apply(relation_rng(X4),sK8(X5,X6))
| in(sK7(X5,X6),X6)
| sP0(X5,X6)
| ~ empty(X4) )
| ~ spl22_35
| ~ spl22_181 ),
inference(resolution,[],[f1682,f390]) ).
fof(f6153,plain,
( spl22_440
| ~ spl22_153
| ~ spl22_177 ),
inference(avatar_split_clause,[],[f1663,f1652,f1395,f6151]) ).
fof(f1652,plain,
( spl22_177
<=> ! [X6,X5] :
( sK7(X5,X6) = apply(X5,sK8(X5,X6))
| sP0(X5,X6)
| ~ in(X6,sK7(X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_177])]) ).
fof(f1663,plain,
( ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| sK7(X0,apply(X1,X2)) = apply(X0,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK7(X0,apply(X1,X2))) )
| ~ spl22_153
| ~ spl22_177 ),
inference(resolution,[],[f1653,f1396]) ).
fof(f1653,plain,
( ! [X6,X5] :
( ~ in(X6,sK7(X5,X6))
| sP0(X5,X6)
| sK7(X5,X6) = apply(X5,sK8(X5,X6)) )
| ~ spl22_177 ),
inference(avatar_component_clause,[],[f1652]) ).
fof(f6149,plain,
( spl22_439
| ~ spl22_76
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1631,f1558,f684,f6147]) ).
fof(f6147,plain,
( spl22_439
<=> ! [X9,X7,X6,X8] :
( element(sK13(X6,X7,X8),X6)
| sP2(X6,X7,X8)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_439])]) ).
fof(f1631,plain,
( ! [X8,X6,X9,X7] :
( element(sK13(X6,X7,X8),X6)
| sP2(X6,X7,X8)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) )
| ~ spl22_76
| ~ spl22_172 ),
inference(resolution,[],[f1559,f685]) ).
fof(f6145,plain,
( spl22_438
| ~ spl22_76
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1616,f1550,f684,f6143]) ).
fof(f6143,plain,
( spl22_438
<=> ! [X5,X7,X6,X8] :
( element(sK13(X5,X6,X7),X7)
| sP2(X5,X6,X7)
| apply(X8,sK13(X5,X6,X7)) = apply(relation_dom_restriction(X8,X5),sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_438])]) ).
fof(f1616,plain,
( ! [X8,X6,X7,X5] :
( element(sK13(X5,X6,X7),X7)
| sP2(X5,X6,X7)
| apply(X8,sK13(X5,X6,X7)) = apply(relation_dom_restriction(X8,X5),sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) )
| ~ spl22_76
| ~ spl22_170 ),
inference(resolution,[],[f1551,f685]) ).
fof(f6141,plain,
( spl22_437
| ~ spl22_76
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1601,f1542,f684,f6139]) ).
fof(f6139,plain,
( spl22_437
<=> ! [X9,X7,X6,X8] :
( element(sK13(X6,X7,X8),X7)
| sP2(X6,X7,X8)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_437])]) ).
fof(f1601,plain,
( ! [X8,X6,X9,X7] :
( element(sK13(X6,X7,X8),X7)
| sP2(X6,X7,X8)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) )
| ~ spl22_76
| ~ spl22_168 ),
inference(resolution,[],[f1543,f685]) ).
fof(f6137,plain,
( spl22_436
| ~ spl22_250
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4500,f3672,f2571,f6135]) ).
fof(f6135,plain,
( spl22_436
<=> ! [X13,X12] :
( ~ sP0(sK5,relation_dom(X12))
| ~ sP0(X12,X13)
| ~ empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_436])]) ).
fof(f4500,plain,
( ! [X12,X13] :
( ~ sP0(sK5,relation_dom(X12))
| ~ sP0(X12,X13)
| ~ empty(X13) )
| ~ spl22_250
| ~ spl22_340 ),
inference(resolution,[],[f3673,f2572]) ).
fof(f6133,plain,
( spl22_435
| ~ spl22_76
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1581,f1533,f684,f6131]) ).
fof(f6131,plain,
( spl22_435
<=> ! [X5,X7,X6,X8] :
( element(sK13(X5,X6,X7),X7)
| sP2(X5,X6,X7)
| apply(relation_dom_restriction(X8,X6),sK13(X5,X6,X7)) = apply(X8,sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_435])]) ).
fof(f1581,plain,
( ! [X8,X6,X7,X5] :
( element(sK13(X5,X6,X7),X7)
| sP2(X5,X6,X7)
| apply(relation_dom_restriction(X8,X6),sK13(X5,X6,X7)) = apply(X8,sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) )
| ~ spl22_76
| ~ spl22_166 ),
inference(resolution,[],[f1534,f685]) ).
fof(f6129,plain,
( spl22_434
| ~ spl22_83
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1328,f1304,f740,f6127]) ).
fof(f6127,plain,
( spl22_434
<=> ! [X9,X11,X10] :
( empty(powerset(X9))
| ~ subset(sK13(X10,X11,powerset(X9)),X9)
| ~ in(sK13(X10,X11,powerset(X9)),X10)
| ~ in(sK13(X10,X11,powerset(X9)),X11)
| sP2(X10,X11,powerset(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_434])]) ).
fof(f1328,plain,
( ! [X10,X11,X9] :
( empty(powerset(X9))
| ~ subset(sK13(X10,X11,powerset(X9)),X9)
| ~ in(sK13(X10,X11,powerset(X9)),X10)
| ~ in(sK13(X10,X11,powerset(X9)),X11)
| sP2(X10,X11,powerset(X9)) )
| ~ spl22_83
| ~ spl22_143 ),
inference(resolution,[],[f1305,f741]) ).
fof(f6109,plain,
( spl22_433
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1881,f1784,f812,f249,f433,f6107]) ).
fof(f6107,plain,
( spl22_433
<=> ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X15),sK7(X14,X15)) = apply(sK15,sK7(X14,X15))
| sK7(X14,X15) = apply(X14,sK8(X14,X15))
| sP0(X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_433])]) ).
fof(f1881,plain,
( ! [X14,X15] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X15),sK7(X14,X15)) = apply(sK15,sK7(X14,X15))
| sP0(X14,X15)
| sK7(X14,X15) = apply(X14,sK8(X14,X15)) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_190 ),
inference(forward_demodulation,[],[f1880,f814]) ).
fof(f1880,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X15),sK7(X14,X15)) = apply(sK15,sK7(X14,X15))
| sP0(X14,X15)
| ~ function(empty_set)
| sK7(X14,X15) = apply(X14,sK8(X14,X15)) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_190 ),
inference(forward_demodulation,[],[f1871,f814]) ).
fof(f1871,plain,
( ! [X14,X15] :
( sP0(X14,X15)
| apply(relation_dom_restriction(empty_set,X15),sK7(X14,X15)) = apply(empty_set,sK7(X14,X15))
| ~ function(empty_set)
| sK7(X14,X15) = apply(X14,sK8(X14,X15)) )
| ~ spl22_7
| ~ spl22_190 ),
inference(resolution,[],[f1785,f251]) ).
fof(f6089,plain,
( ~ spl22_20
| spl22_432
| ~ spl22_19
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1878,f1784,f309,f6087,f314]) ).
fof(f6087,plain,
( spl22_432
<=> ! [X29,X28] :
( sP0(X28,X29)
| sK7(X28,X29) = apply(X28,sK8(X28,X29))
| apply(relation_dom_restriction(sK20,X29),sK7(X28,X29)) = apply(sK20,sK7(X28,X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_432])]) ).
fof(f1878,plain,
( ! [X28,X29] :
( sP0(X28,X29)
| apply(relation_dom_restriction(sK20,X29),sK7(X28,X29)) = apply(sK20,sK7(X28,X29))
| ~ function(sK20)
| sK7(X28,X29) = apply(X28,sK8(X28,X29)) )
| ~ spl22_19
| ~ spl22_190 ),
inference(resolution,[],[f1785,f311]) ).
fof(f6069,plain,
( ~ spl22_18
| spl22_431
| ~ spl22_17
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1877,f1784,f299,f6067,f304]) ).
fof(f1877,plain,
( ! [X26,X27] :
( sP0(X26,X27)
| apply(relation_dom_restriction(sK19,X27),sK7(X26,X27)) = apply(sK19,sK7(X26,X27))
| ~ function(sK19)
| sK7(X26,X27) = apply(X26,sK8(X26,X27)) )
| ~ spl22_17
| ~ spl22_190 ),
inference(resolution,[],[f1785,f301]) ).
fof(f6032,plain,
( spl22_430
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1862,f1780,f812,f249,f433,f6030]) ).
fof(f1862,plain,
( ! [X18,X19,X20] :
( ~ function(sK15)
| apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X18),sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| in(sK13(X18,X19,X20),X20) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_189 ),
inference(forward_demodulation,[],[f1861,f814]) ).
fof(f1861,plain,
( ! [X18,X19,X20] :
( apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X18),sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X20) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_189 ),
inference(forward_demodulation,[],[f1852,f814]) ).
fof(f1852,plain,
( ! [X18,X19,X20] :
( sP2(X18,X19,X20)
| apply(empty_set,sK13(X18,X19,X20)) = apply(relation_dom_restriction(empty_set,X18),sK13(X18,X19,X20))
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X20) )
| ~ spl22_7
| ~ spl22_189 ),
inference(resolution,[],[f1781,f251]) ).
fof(f5993,plain,
( ~ spl22_20
| spl22_429
| ~ spl22_19
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1859,f1780,f309,f5991,f314]) ).
fof(f1859,plain,
( ! [X40,X41,X39] :
( sP2(X39,X40,X41)
| apply(sK20,sK13(X39,X40,X41)) = apply(relation_dom_restriction(sK20,X39),sK13(X39,X40,X41))
| ~ function(sK20)
| in(sK13(X39,X40,X41),X41) )
| ~ spl22_19
| ~ spl22_189 ),
inference(resolution,[],[f1781,f311]) ).
fof(f5956,plain,
( ~ spl22_18
| spl22_428
| ~ spl22_17
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1858,f1780,f299,f5954,f304]) ).
fof(f1858,plain,
( ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| apply(sK19,sK13(X36,X37,X38)) = apply(relation_dom_restriction(sK19,X36),sK13(X36,X37,X38))
| ~ function(sK19)
| in(sK13(X36,X37,X38),X38) )
| ~ spl22_17
| ~ spl22_189 ),
inference(resolution,[],[f1781,f301]) ).
fof(f5919,plain,
( spl22_427
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1843,f1776,f812,f249,f433,f5917]) ).
fof(f1843,plain,
( ! [X18,X19,X20] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| in(sK13(X18,X19,X20),X18) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_188 ),
inference(forward_demodulation,[],[f1842,f814]) ).
fof(f1842,plain,
( ! [X18,X19,X20] :
( apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X18) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_188 ),
inference(forward_demodulation,[],[f1833,f814]) ).
fof(f1833,plain,
( ! [X18,X19,X20] :
( sP2(X18,X19,X20)
| apply(relation_dom_restriction(empty_set,X20),sK13(X18,X19,X20)) = apply(empty_set,sK13(X18,X19,X20))
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X18) )
| ~ spl22_7
| ~ spl22_188 ),
inference(resolution,[],[f1777,f251]) ).
fof(f5882,plain,
( ~ spl22_20
| spl22_426
| ~ spl22_19
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1840,f1776,f309,f5880,f314]) ).
fof(f1840,plain,
( ! [X40,X41,X39] :
( sP2(X39,X40,X41)
| apply(relation_dom_restriction(sK20,X41),sK13(X39,X40,X41)) = apply(sK20,sK13(X39,X40,X41))
| ~ function(sK20)
| in(sK13(X39,X40,X41),X39) )
| ~ spl22_19
| ~ spl22_188 ),
inference(resolution,[],[f1777,f311]) ).
fof(f5845,plain,
( ~ spl22_18
| spl22_425
| ~ spl22_17
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1839,f1776,f299,f5843,f304]) ).
fof(f1839,plain,
( ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| apply(relation_dom_restriction(sK19,X38),sK13(X36,X37,X38)) = apply(sK19,sK13(X36,X37,X38))
| ~ function(sK19)
| in(sK13(X36,X37,X38),X36) )
| ~ spl22_17
| ~ spl22_188 ),
inference(resolution,[],[f1777,f301]) ).
fof(f5841,plain,
( ~ spl22_424
| ~ spl22_340
| ~ spl22_410 ),
inference(avatar_split_clause,[],[f5651,f5366,f3672,f5838]) ).
fof(f5838,plain,
( spl22_424
<=> sP0(sK5,sK7(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_424])]) ).
fof(f5366,plain,
( spl22_410
<=> ! [X4] :
( ~ sP0(sK5,X4)
| ~ in(X4,sK7(sK5,sK15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_410])]) ).
fof(f5651,plain,
( ~ sP0(sK5,sK7(sK5,sK15))
| ~ spl22_340
| ~ spl22_410 ),
inference(duplicate_literal_removal,[],[f5610]) ).
fof(f5610,plain,
( ~ sP0(sK5,sK7(sK5,sK15))
| ~ sP0(sK5,sK7(sK5,sK15))
| ~ spl22_340
| ~ spl22_410 ),
inference(resolution,[],[f5367,f3673]) ).
fof(f5367,plain,
( ! [X4] :
( ~ in(X4,sK7(sK5,sK15))
| ~ sP0(sK5,X4) )
| ~ spl22_410 ),
inference(avatar_component_clause,[],[f5366]) ).
fof(f5803,plain,
( spl22_423
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1824,f1772,f812,f249,f433,f5801]) ).
fof(f1824,plain,
( ! [X18,X19,X20] :
( ~ function(sK15)
| apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X19),sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| in(sK13(X18,X19,X20),X20) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_187 ),
inference(forward_demodulation,[],[f1823,f814]) ).
fof(f1823,plain,
( ! [X18,X19,X20] :
( apply(sK15,sK13(X18,X19,X20)) = apply(relation_dom_restriction(sK15,X19),sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X20) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_187 ),
inference(forward_demodulation,[],[f1814,f814]) ).
fof(f1814,plain,
( ! [X18,X19,X20] :
( sP2(X18,X19,X20)
| apply(empty_set,sK13(X18,X19,X20)) = apply(relation_dom_restriction(empty_set,X19),sK13(X18,X19,X20))
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X20) )
| ~ spl22_7
| ~ spl22_187 ),
inference(resolution,[],[f1773,f251]) ).
fof(f5766,plain,
( ~ spl22_20
| spl22_422
| ~ spl22_19
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1821,f1772,f309,f5764,f314]) ).
fof(f1821,plain,
( ! [X40,X41,X39] :
( sP2(X39,X40,X41)
| apply(sK20,sK13(X39,X40,X41)) = apply(relation_dom_restriction(sK20,X40),sK13(X39,X40,X41))
| ~ function(sK20)
| in(sK13(X39,X40,X41),X41) )
| ~ spl22_19
| ~ spl22_187 ),
inference(resolution,[],[f1773,f311]) ).
fof(f5729,plain,
( ~ spl22_18
| spl22_421
| ~ spl22_17
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1820,f1772,f299,f5727,f304]) ).
fof(f1820,plain,
( ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| apply(sK19,sK13(X36,X37,X38)) = apply(relation_dom_restriction(sK19,X37),sK13(X36,X37,X38))
| ~ function(sK19)
| in(sK13(X36,X37,X38),X38) )
| ~ spl22_17
| ~ spl22_187 ),
inference(resolution,[],[f1773,f301]) ).
fof(f5692,plain,
( spl22_420
| ~ spl22_42
| ~ spl22_7
| ~ spl22_94
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1805,f1768,f812,f249,f433,f5690]) ).
fof(f1805,plain,
( ! [X18,X19,X20] :
( ~ function(sK15)
| apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| in(sK13(X18,X19,X20),X19) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_186 ),
inference(forward_demodulation,[],[f1804,f814]) ).
fof(f1804,plain,
( ! [X18,X19,X20] :
( apply(relation_dom_restriction(sK15,X20),sK13(X18,X19,X20)) = apply(sK15,sK13(X18,X19,X20))
| sP2(X18,X19,X20)
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X19) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_186 ),
inference(forward_demodulation,[],[f1795,f814]) ).
fof(f1795,plain,
( ! [X18,X19,X20] :
( sP2(X18,X19,X20)
| apply(relation_dom_restriction(empty_set,X20),sK13(X18,X19,X20)) = apply(empty_set,sK13(X18,X19,X20))
| ~ function(empty_set)
| in(sK13(X18,X19,X20),X19) )
| ~ spl22_7
| ~ spl22_186 ),
inference(resolution,[],[f1769,f251]) ).
fof(f5655,plain,
( ~ spl22_20
| spl22_419
| ~ spl22_19
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1802,f1768,f309,f5653,f314]) ).
fof(f1802,plain,
( ! [X40,X41,X39] :
( sP2(X39,X40,X41)
| apply(relation_dom_restriction(sK20,X41),sK13(X39,X40,X41)) = apply(sK20,sK13(X39,X40,X41))
| ~ function(sK20)
| in(sK13(X39,X40,X41),X40) )
| ~ spl22_19
| ~ spl22_186 ),
inference(resolution,[],[f1769,f311]) ).
fof(f5568,plain,
( ~ spl22_18
| spl22_418
| ~ spl22_17
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1801,f1768,f299,f5566,f304]) ).
fof(f1801,plain,
( ! [X38,X36,X37] :
( sP2(X36,X37,X38)
| apply(relation_dom_restriction(sK19,X38),sK13(X36,X37,X38)) = apply(sK19,sK13(X36,X37,X38))
| ~ function(sK19)
| in(sK13(X36,X37,X38),X37) )
| ~ spl22_17
| ~ spl22_186 ),
inference(resolution,[],[f1769,f301]) ).
fof(f5480,plain,
( spl22_417
| ~ spl22_153
| ~ spl22_173 ),
inference(avatar_split_clause,[],[f1639,f1562,f1395,f5478]) ).
fof(f1562,plain,
( spl22_173
<=> ! [X9,X8,X7] :
( in(sK13(X7,X8,X9),X9)
| sP2(X7,X8,X9)
| ~ in(X7,sK13(X7,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_173])]) ).
fof(f1639,plain,
( ! [X2,X3,X0,X1] :
( sP2(apply(X0,X1),X2,X3)
| in(sK13(apply(X0,X1),X2,X3),X3)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,sK13(apply(X0,X1),X2,X3)) )
| ~ spl22_153
| ~ spl22_173 ),
inference(resolution,[],[f1563,f1396]) ).
fof(f1563,plain,
( ! [X8,X9,X7] :
( ~ in(X7,sK13(X7,X8,X9))
| sP2(X7,X8,X9)
| in(sK13(X7,X8,X9),X9) )
| ~ spl22_173 ),
inference(avatar_component_clause,[],[f1562]) ).
fof(f5476,plain,
( spl22_416
| ~ spl22_153
| ~ spl22_171 ),
inference(avatar_split_clause,[],[f1624,f1554,f1395,f5474]) ).
fof(f1554,plain,
( spl22_171
<=> ! [X9,X7,X8] :
( in(sK13(X7,X8,X9),X7)
| sP2(X7,X8,X9)
| ~ in(X9,sK13(X7,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_171])]) ).
fof(f1624,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| in(sK13(X0,X1,apply(X2,X3)),X0)
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3))) )
| ~ spl22_153
| ~ spl22_171 ),
inference(resolution,[],[f1555,f1396]) ).
fof(f1555,plain,
( ! [X8,X9,X7] :
( ~ in(X9,sK13(X7,X8,X9))
| sP2(X7,X8,X9)
| in(sK13(X7,X8,X9),X7) )
| ~ spl22_171 ),
inference(avatar_component_clause,[],[f1554]) ).
fof(f5468,plain,
( spl22_415
| ~ spl22_153
| ~ spl22_169 ),
inference(avatar_split_clause,[],[f1609,f1546,f1395,f5466]) ).
fof(f1546,plain,
( spl22_169
<=> ! [X9,X8,X7] :
( in(sK13(X7,X8,X9),X9)
| sP2(X7,X8,X9)
| ~ in(X8,sK13(X7,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_169])]) ).
fof(f1609,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,apply(X1,X2),X3)
| in(sK13(X0,apply(X1,X2),X3),X3)
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK13(X0,apply(X1,X2),X3)) )
| ~ spl22_153
| ~ spl22_169 ),
inference(resolution,[],[f1547,f1396]) ).
fof(f1547,plain,
( ! [X8,X9,X7] :
( ~ in(X8,sK13(X7,X8,X9))
| sP2(X7,X8,X9)
| in(sK13(X7,X8,X9),X9) )
| ~ spl22_169 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f5464,plain,
( spl22_414
| ~ spl22_153
| ~ spl22_167 ),
inference(avatar_split_clause,[],[f1589,f1537,f1395,f5462]) ).
fof(f1537,plain,
( spl22_167
<=> ! [X9,X8,X7] :
( in(sK13(X7,X8,X9),X8)
| sP2(X7,X8,X9)
| ~ in(X9,sK13(X7,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_167])]) ).
fof(f1589,plain,
( ! [X2,X3,X0,X1] :
( sP2(X0,X1,apply(X2,X3))
| in(sK13(X0,X1,apply(X2,X3)),X1)
| ~ in(X3,relation_dom(X2))
| ~ sP0(X2,sK13(X0,X1,apply(X2,X3))) )
| ~ spl22_153
| ~ spl22_167 ),
inference(resolution,[],[f1538,f1396]) ).
fof(f1538,plain,
( ! [X8,X9,X7] :
( ~ in(X9,sK13(X7,X8,X9))
| sP2(X7,X8,X9)
| in(sK13(X7,X8,X9),X8) )
| ~ spl22_167 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f5460,plain,
( spl22_413
| ~ spl22_76
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1517,f1489,f684,f5458]) ).
fof(f5458,plain,
( spl22_413
<=> ! [X2,X4,X3] :
( element(sK7(X2,X3),X3)
| sP0(X2,X3)
| apply(relation_dom_restriction(X4,relation_dom(X2)),sK8(X2,X3)) = apply(X4,sK8(X2,X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_413])]) ).
fof(f1517,plain,
( ! [X2,X3,X4] :
( element(sK7(X2,X3),X3)
| sP0(X2,X3)
| apply(relation_dom_restriction(X4,relation_dom(X2)),sK8(X2,X3)) = apply(X4,sK8(X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_76
| ~ spl22_161 ),
inference(resolution,[],[f1490,f685]) ).
fof(f5456,plain,
( spl22_412
| ~ spl22_76
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1509,f1481,f684,f5454]) ).
fof(f5454,plain,
( spl22_412
<=> ! [X2,X4,X3] :
( element(sK8(X2,X3),relation_dom(X2))
| sP0(X2,X3)
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_412])]) ).
fof(f1509,plain,
( ! [X2,X3,X4] :
( element(sK8(X2,X3),relation_dom(X2))
| sP0(X2,X3)
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_76
| ~ spl22_159 ),
inference(resolution,[],[f1482,f685]) ).
fof(f5372,plain,
( spl22_411
| ~ spl22_76
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1468,f1411,f684,f5370]) ).
fof(f5370,plain,
( spl22_411
<=> ! [X9,X7,X6,X8] :
( sP2(X6,X7,X8)
| ~ empty(X6)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_411])]) ).
fof(f1468,plain,
( ! [X8,X6,X9,X7] :
( sP2(X6,X7,X8)
| ~ empty(X6)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) )
| ~ spl22_76
| ~ spl22_157 ),
inference(resolution,[],[f1412,f685]) ).
fof(f5368,plain,
( spl22_410
| ~ spl22_45
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4495,f3672,f448,f5366]) ).
fof(f4495,plain,
( ! [X4] :
( ~ sP0(sK5,X4)
| ~ in(X4,sK7(sK5,sK15)) )
| ~ spl22_45
| ~ spl22_340 ),
inference(resolution,[],[f3673,f449]) ).
fof(f5364,plain,
( spl22_409
| ~ spl22_76
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1458,f1407,f684,f5362]) ).
fof(f5362,plain,
( spl22_409
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| ~ empty(X7)
| apply(X8,sK13(X5,X6,X7)) = apply(relation_dom_restriction(X8,X5),sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_409])]) ).
fof(f1458,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| ~ empty(X7)
| apply(X8,sK13(X5,X6,X7)) = apply(relation_dom_restriction(X8,X5),sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) )
| ~ spl22_76
| ~ spl22_156 ),
inference(resolution,[],[f1408,f685]) ).
fof(f5360,plain,
( spl22_408
| ~ spl22_76
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1448,f1403,f684,f5358]) ).
fof(f5358,plain,
( spl22_408
<=> ! [X9,X7,X6,X8] :
( sP2(X6,X7,X8)
| ~ empty(X7)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_408])]) ).
fof(f1448,plain,
( ! [X8,X6,X9,X7] :
( sP2(X6,X7,X8)
| ~ empty(X7)
| apply(relation_dom_restriction(X9,X8),sK13(X6,X7,X8)) = apply(X9,sK13(X6,X7,X8))
| ~ function(X9)
| ~ relation(X9) )
| ~ spl22_76
| ~ spl22_155 ),
inference(resolution,[],[f1404,f685]) ).
fof(f5356,plain,
( spl22_407
| ~ spl22_76
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1438,f1399,f684,f5354]) ).
fof(f5354,plain,
( spl22_407
<=> ! [X5,X7,X6,X8] :
( sP2(X5,X6,X7)
| ~ empty(X7)
| apply(relation_dom_restriction(X8,X6),sK13(X5,X6,X7)) = apply(X8,sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_407])]) ).
fof(f1438,plain,
( ! [X8,X6,X7,X5] :
( sP2(X5,X6,X7)
| ~ empty(X7)
| apply(relation_dom_restriction(X8,X6),sK13(X5,X6,X7)) = apply(X8,sK13(X5,X6,X7))
| ~ function(X8)
| ~ relation(X8) )
| ~ spl22_76
| ~ spl22_154 ),
inference(resolution,[],[f1400,f685]) ).
fof(f5352,plain,
( spl22_406
| ~ spl22_79
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1256,f1213,f718,f5350]) ).
fof(f5350,plain,
( spl22_406
<=> ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| sP0(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_406])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( element(sK7(X0,sK10(powerset(X1))),X1)
| sK7(X0,sK10(powerset(X1))) = apply(X0,sK8(X0,sK10(powerset(X1))))
| sP0(X0,sK10(powerset(X1))) )
| ~ spl22_79
| ~ spl22_137 ),
inference(resolution,[],[f1214,f719]) ).
fof(f5213,plain,
( ~ spl22_42
| spl22_405
| ~ spl22_7
| ~ spl22_94
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1730,f1685,f812,f249,f5211,f433]) ).
fof(f1730,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(sK15,X14),sK7(X15,X14)) = apply(sK15,sK7(X15,X14))
| ~ function(sK15)
| in(sK8(X15,X14),relation_dom(X15))
| sP0(X15,X14) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_182 ),
inference(forward_demodulation,[],[f1729,f814]) ).
fof(f1729,plain,
( ! [X14,X15] :
( ~ function(sK15)
| apply(relation_dom_restriction(empty_set,X14),sK7(X15,X14)) = apply(empty_set,sK7(X15,X14))
| in(sK8(X15,X14),relation_dom(X15))
| sP0(X15,X14) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_182 ),
inference(forward_demodulation,[],[f1720,f814]) ).
fof(f1720,plain,
( ! [X14,X15] :
( ~ function(empty_set)
| apply(relation_dom_restriction(empty_set,X14),sK7(X15,X14)) = apply(empty_set,sK7(X15,X14))
| in(sK8(X15,X14),relation_dom(X15))
| sP0(X15,X14) )
| ~ spl22_7
| ~ spl22_182 ),
inference(resolution,[],[f1686,f251]) ).
fof(f5201,plain,
( spl22_404
| ~ spl22_46
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4494,f3672,f452,f5199]) ).
fof(f4494,plain,
( ! [X3] :
( ~ sP0(sK5,X3)
| element(sK7(sK5,sK15),X3) )
| ~ spl22_46
| ~ spl22_340 ),
inference(resolution,[],[f3673,f453]) ).
fof(f5197,plain,
( spl22_403
| ~ spl22_20
| ~ spl22_19
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1727,f1685,f309,f314,f5195]) ).
fof(f1727,plain,
( ! [X28,X29] :
( ~ function(sK20)
| apply(relation_dom_restriction(sK20,X28),sK7(X29,X28)) = apply(sK20,sK7(X29,X28))
| in(sK8(X29,X28),relation_dom(X29))
| sP0(X29,X28) )
| ~ spl22_19
| ~ spl22_182 ),
inference(resolution,[],[f1686,f311]) ).
fof(f5185,plain,
( spl22_402
| ~ spl22_18
| ~ spl22_17
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1726,f1685,f299,f304,f5183]) ).
fof(f1726,plain,
( ! [X26,X27] :
( ~ function(sK19)
| apply(relation_dom_restriction(sK19,X26),sK7(X27,X26)) = apply(sK19,sK7(X27,X26))
| in(sK8(X27,X26),relation_dom(X27))
| sP0(X27,X26) )
| ~ spl22_17
| ~ spl22_182 ),
inference(resolution,[],[f1686,f301]) ).
fof(f5155,plain,
( ~ spl22_42
| spl22_401
| ~ spl22_7
| ~ spl22_94
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1711,f1681,f812,f249,f5153,f433]) ).
fof(f1711,plain,
( ! [X14,X15] :
( apply(relation_dom_restriction(sK15,relation_dom(X14)),sK8(X14,X15)) = apply(sK15,sK8(X14,X15))
| ~ function(sK15)
| in(sK7(X14,X15),X15)
| sP0(X14,X15) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_181 ),
inference(forward_demodulation,[],[f1710,f814]) ).
fof(f1710,plain,
( ! [X14,X15] :
( ~ function(sK15)
| apply(relation_dom_restriction(empty_set,relation_dom(X14)),sK8(X14,X15)) = apply(empty_set,sK8(X14,X15))
| in(sK7(X14,X15),X15)
| sP0(X14,X15) )
| ~ spl22_7
| ~ spl22_94
| ~ spl22_181 ),
inference(forward_demodulation,[],[f1701,f814]) ).
fof(f1701,plain,
( ! [X14,X15] :
( ~ function(empty_set)
| apply(relation_dom_restriction(empty_set,relation_dom(X14)),sK8(X14,X15)) = apply(empty_set,sK8(X14,X15))
| in(sK7(X14,X15),X15)
| sP0(X14,X15) )
| ~ spl22_7
| ~ spl22_181 ),
inference(resolution,[],[f1682,f251]) ).
fof(f5125,plain,
( spl22_400
| ~ spl22_20
| ~ spl22_19
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1708,f1681,f309,f314,f5123]) ).
fof(f1708,plain,
( ! [X28,X29] :
( ~ function(sK20)
| apply(relation_dom_restriction(sK20,relation_dom(X28)),sK8(X28,X29)) = apply(sK20,sK8(X28,X29))
| in(sK7(X28,X29),X29)
| sP0(X28,X29) )
| ~ spl22_19
| ~ spl22_181 ),
inference(resolution,[],[f1682,f311]) ).
fof(f5095,plain,
( spl22_399
| ~ spl22_18
| ~ spl22_17
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1707,f1681,f299,f304,f5093]) ).
fof(f1707,plain,
( ! [X26,X27] :
( ~ function(sK19)
| apply(relation_dom_restriction(sK19,relation_dom(X26)),sK8(X26,X27)) = apply(sK19,sK8(X26,X27))
| in(sK7(X26,X27),X27)
| sP0(X26,X27) )
| ~ spl22_17
| ~ spl22_181 ),
inference(resolution,[],[f1682,f301]) ).
fof(f5091,plain,
( spl22_398
| ~ spl22_67
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1656,f1648,f633,f5089]) ).
fof(f1648,plain,
( spl22_176
<=> ! [X4,X3] :
( sK7(X3,X4) = apply(X3,sK8(X3,X4))
| sP0(X3,X4)
| element(sK7(X3,X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_176])]) ).
fof(f1656,plain,
( ! [X3,X4,X5] :
( sP0(X3,powerset(X4))
| sK7(X3,powerset(X4)) = apply(X3,sK8(X3,powerset(X4)))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) )
| ~ spl22_67
| ~ spl22_176 ),
inference(resolution,[],[f1649,f634]) ).
fof(f1649,plain,
( ! [X3,X4] :
( element(sK7(X3,X4),X4)
| sP0(X3,X4)
| sK7(X3,X4) = apply(X3,sK8(X3,X4)) )
| ~ spl22_176 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f5081,plain,
( spl22_397
| ~ spl22_153
| ~ spl22_162 ),
inference(avatar_split_clause,[],[f1524,f1493,f1395,f5079]) ).
fof(f1493,plain,
( spl22_162
<=> ! [X2,X3] :
( in(sK8(X2,X3),relation_dom(X2))
| sP0(X2,X3)
| ~ in(X3,sK7(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_162])]) ).
fof(f1524,plain,
( ! [X2,X0,X1] :
( sP0(X0,apply(X1,X2))
| in(sK8(X0,apply(X1,X2)),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP0(X1,sK7(X0,apply(X1,X2))) )
| ~ spl22_153
| ~ spl22_162 ),
inference(resolution,[],[f1494,f1396]) ).
fof(f1494,plain,
( ! [X2,X3] :
( ~ in(X3,sK7(X2,X3))
| sP0(X2,X3)
| in(sK8(X2,X3),relation_dom(X2)) )
| ~ spl22_162 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f5077,plain,
( spl22_396
| ~ spl22_76
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1425,f1395,f684,f5075]) ).
fof(f1425,plain,
( ! [X3,X6,X4,X5] :
( ~ in(X3,relation_dom(X4))
| ~ sP0(X4,X5)
| apply(relation_dom_restriction(X6,X5),apply(X4,X3)) = apply(X6,apply(X4,X3))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_76
| ~ spl22_153 ),
inference(resolution,[],[f1396,f685]) ).
fof(f4963,plain,
( spl22_395
| ~ spl22_65
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1655,f1648,f610,f4961]) ).
fof(f1655,plain,
( ! [X2,X0,X1] :
( sP0(X0,powerset(X1))
| sK7(X0,powerset(X1)) = apply(X0,sK8(X0,powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_176 ),
inference(resolution,[],[f1649,f611]) ).
fof(f4959,plain,
( spl22_394
| ~ spl22_76
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1387,f1366,f684,f4957]) ).
fof(f4957,plain,
( spl22_394
<=> ! [X2,X4,X3] :
( sP0(X2,X3)
| ~ empty(X3)
| apply(relation_dom_restriction(X4,relation_dom(X2)),sK8(X2,X3)) = apply(X4,sK8(X2,X3))
| ~ function(X4)
| ~ relation(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_394])]) ).
fof(f1387,plain,
( ! [X2,X3,X4] :
( sP0(X2,X3)
| ~ empty(X3)
| apply(relation_dom_restriction(X4,relation_dom(X2)),sK8(X2,X3)) = apply(X4,sK8(X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_76
| ~ spl22_150 ),
inference(resolution,[],[f1367,f685]) ).
fof(f4952,plain,
( spl22_393
| ~ spl22_76
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1379,f1362,f684,f4950]) ).
fof(f1379,plain,
( ! [X2,X3,X4] :
( sP0(X2,X3)
| ~ empty(relation_dom(X2))
| apply(relation_dom_restriction(X4,X3),sK7(X2,X3)) = apply(X4,sK7(X2,X3))
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_76
| ~ spl22_149 ),
inference(resolution,[],[f1363,f685]) ).
fof(f4948,plain,
( spl22_392
| ~ spl22_76
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1345,f1316,f684,f4946]) ).
fof(f1345,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X4)
| apply(relation_dom_restriction(X6,X4),sK13(X4,X5,X4)) = apply(X6,sK13(X4,X5,X4))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_76
| ~ spl22_146 ),
inference(resolution,[],[f1317,f685]) ).
fof(f4944,plain,
( spl22_391
| ~ spl22_76
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1335,f1312,f684,f4942]) ).
fof(f1335,plain,
( ! [X6,X4,X5] :
( sP2(X4,X5,X5)
| apply(relation_dom_restriction(X6,X5),sK13(X4,X5,X5)) = apply(X6,sK13(X4,X5,X5))
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_76
| ~ spl22_145 ),
inference(resolution,[],[f1313,f685]) ).
fof(f4940,plain,
( spl22_390
| ~ spl22_79
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1292,f1277,f718,f4938]) ).
fof(f1292,plain,
( ! [X0,X1] :
( element(sK7(X0,sK6(X1)),X1)
| empty(X1)
| sK7(X0,sK6(X1)) = apply(X0,sK8(X0,sK6(X1)))
| sP0(X0,sK6(X1)) )
| ~ spl22_79
| ~ spl22_141 ),
inference(resolution,[],[f1278,f719]) ).
fof(f4771,plain,
( spl22_389
| ~ spl22_131
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4511,f3672,f1173,f4769]) ).
fof(f4769,plain,
( spl22_389
<=> ! [X27] :
( ~ sP0(sK5,sK10(powerset(X27)))
| ~ empty(X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_389])]) ).
fof(f4511,plain,
( ! [X27] :
( ~ sP0(sK5,sK10(powerset(X27)))
| ~ empty(X27) )
| ~ spl22_131
| ~ spl22_340 ),
inference(resolution,[],[f3673,f1174]) ).
fof(f4596,plain,
( spl22_388
| ~ spl22_137
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1635,f1558,f1213,f4594]) ).
fof(f1635,plain,
( ! [X21,X19,X20] :
( element(sK13(X19,X20,sK10(powerset(X21))),X19)
| sP2(X19,X20,sK10(powerset(X21)))
| element(sK13(X19,X20,sK10(powerset(X21))),X21) )
| ~ spl22_137
| ~ spl22_172 ),
inference(resolution,[],[f1559,f1214]) ).
fof(f4592,plain,
( spl22_387
| ~ spl22_67
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1626,f1558,f633,f4590]) ).
fof(f1626,plain,
( ! [X6,X7,X4,X5] :
( in(sK13(powerset(X4),X5,X6),X6)
| sP2(powerset(X4),X5,X6)
| element(X7,X4)
| ~ in(X7,sK13(powerset(X4),X5,X6)) )
| ~ spl22_67
| ~ spl22_172 ),
inference(resolution,[],[f1559,f634]) ).
fof(f4588,plain,
( spl22_386
| ~ spl22_137
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1620,f1550,f1213,f4586]) ).
fof(f1620,plain,
( ! [X18,X19,X20] :
( element(sK13(sK10(powerset(X18)),X19,X20),X20)
| sP2(sK10(powerset(X18)),X19,X20)
| element(sK13(sK10(powerset(X18)),X19,X20),X18) )
| ~ spl22_137
| ~ spl22_170 ),
inference(resolution,[],[f1551,f1214]) ).
fof(f4584,plain,
( spl22_385
| ~ spl22_67
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1611,f1550,f633,f4582]) ).
fof(f1611,plain,
( ! [X6,X7,X4,X5] :
( in(sK13(X4,X5,powerset(X6)),X4)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) )
| ~ spl22_67
| ~ spl22_170 ),
inference(resolution,[],[f1551,f634]) ).
fof(f4580,plain,
( spl22_384
| ~ spl22_236
| ~ spl22_340 ),
inference(avatar_split_clause,[],[f4501,f3672,f2331,f4578]) ).
fof(f4501,plain,
( ! [X14] :
( ~ sP0(sK5,relation_dom(X14))
| ~ sP0(X14,sK15) )
| ~ spl22_236
| ~ spl22_340 ),
inference(resolution,[],[f3673,f2332]) ).
fof(f4576,plain,
( spl22_383
| ~ spl22_137
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1605,f1542,f1213,f4574]) ).
fof(f1605,plain,
( ! [X21,X19,X20] :
( element(sK13(X19,X20,sK10(powerset(X21))),X20)
| sP2(X19,X20,sK10(powerset(X21)))
| element(sK13(X19,X20,sK10(powerset(X21))),X21) )
| ~ spl22_137
| ~ spl22_168 ),
inference(resolution,[],[f1543,f1214]) ).
fof(f4572,plain,
( spl22_382
| ~ spl22_67
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1596,f1542,f633,f4570]) ).
fof(f1596,plain,
( ! [X6,X7,X4,X5] :
( in(sK13(X4,powerset(X5),X6),X6)
| sP2(X4,powerset(X5),X6)
| element(X7,X5)
| ~ in(X7,sK13(X4,powerset(X5),X6)) )
| ~ spl22_67
| ~ spl22_168 ),
inference(resolution,[],[f1543,f634]) ).
fof(f4568,plain,
( spl22_381
| ~ spl22_137
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1585,f1533,f1213,f4566]) ).
fof(f1585,plain,
( ! [X18,X19,X20] :
( element(sK13(X18,sK10(powerset(X19)),X20),X20)
| sP2(X18,sK10(powerset(X19)),X20)
| element(sK13(X18,sK10(powerset(X19)),X20),X19) )
| ~ spl22_137
| ~ spl22_166 ),
inference(resolution,[],[f1534,f1214]) ).
fof(f4564,plain,
( spl22_380
| ~ spl22_67
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1576,f1533,f633,f4562]) ).
fof(f1576,plain,
( ! [X6,X7,X4,X5] :
( in(sK13(X4,X5,powerset(X6)),X5)
| sP2(X4,X5,powerset(X6))
| element(X7,X6)
| ~ in(X7,sK13(X4,X5,powerset(X6))) )
| ~ spl22_67
| ~ spl22_166 ),
inference(resolution,[],[f1534,f634]) ).
fof(f4560,plain,
( spl22_379
| ~ spl22_78
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1262,f1213,f692,f4558]) ).
fof(f1262,plain,
( ! [X16,X14,X15] :
( element(sK13(sK10(powerset(X14)),X15,X16),X14)
| in(sK13(sK10(powerset(X14)),X15,X16),X16)
| sP2(sK10(powerset(X14)),X15,X16) )
| ~ spl22_78
| ~ spl22_137 ),
inference(resolution,[],[f1214,f693]) ).
fof(f4556,plain,
( spl22_378
| ~ spl22_77
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1261,f1213,f688,f4554]) ).
fof(f1261,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK10(powerset(X12)),X13),X12)
| in(sK13(X11,sK10(powerset(X12)),X13),X13)
| sP2(X11,sK10(powerset(X12)),X13) )
| ~ spl22_77
| ~ spl22_137 ),
inference(resolution,[],[f1214,f689]) ).
fof(f4552,plain,
( spl22_377
| ~ spl22_77
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1260,f1213,f688,f4550]) ).
fof(f1260,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK10(powerset(X10))),X10)
| in(sK13(X8,X9,sK10(powerset(X10))),X9)
| sP2(X8,X9,sK10(powerset(X10))) )
| ~ spl22_77
| ~ spl22_137 ),
inference(resolution,[],[f1214,f689]) ).
fof(f4548,plain,
( spl22_376
| ~ spl22_78
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1259,f1213,f692,f4546]) ).
fof(f1259,plain,
( ! [X6,X7,X5] :
( element(sK13(X5,X6,sK10(powerset(X7))),X7)
| in(sK13(X5,X6,sK10(powerset(X7))),X5)
| sP2(X5,X6,sK10(powerset(X7))) )
| ~ spl22_78
| ~ spl22_137 ),
inference(resolution,[],[f1214,f693]) ).
fof(f4174,plain,
( spl22_375
| ~ spl22_52
| ~ spl22_176 ),
inference(avatar_split_clause,[],[f1657,f1648,f498,f4172]) ).
fof(f4172,plain,
( spl22_375
<=> ! [X6,X7] :
( sP0(X6,powerset(X7))
| sK7(X6,powerset(X7)) = apply(X6,sK8(X6,powerset(X7)))
| subset(sK7(X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_375])]) ).
fof(f1657,plain,
( ! [X6,X7] :
( sP0(X6,powerset(X7))
| sK7(X6,powerset(X7)) = apply(X6,sK8(X6,powerset(X7)))
| subset(sK7(X6,powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_176 ),
inference(resolution,[],[f1649,f499]) ).
fof(f4170,plain,
( spl22_374
| ~ spl22_141
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1634,f1558,f1277,f4168]) ).
fof(f1634,plain,
( ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X16)
| sP2(X16,X17,sK6(X18))
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) )
| ~ spl22_141
| ~ spl22_172 ),
inference(resolution,[],[f1559,f1278]) ).
fof(f4166,plain,
( spl22_373
| ~ spl22_65
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1625,f1558,f610,f4164]) ).
fof(f1625,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(powerset(X0),X1,X2),X2)
| sP2(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK13(powerset(X0),X1,X2)) )
| ~ spl22_65
| ~ spl22_172 ),
inference(resolution,[],[f1559,f611]) ).
fof(f4162,plain,
( spl22_372
| ~ spl22_141
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1619,f1550,f1277,f4160]) ).
fof(f1619,plain,
( ! [X16,X17,X15] :
( element(sK13(sK6(X15),X16,X17),X17)
| sP2(sK6(X15),X16,X17)
| element(sK13(sK6(X15),X16,X17),X15)
| empty(X15) )
| ~ spl22_141
| ~ spl22_170 ),
inference(resolution,[],[f1551,f1278]) ).
fof(f4158,plain,
( spl22_371
| ~ spl22_65
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1610,f1550,f610,f4156]) ).
fof(f1610,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,powerset(X2)),X0)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_170 ),
inference(resolution,[],[f1551,f611]) ).
fof(f4154,plain,
( spl22_370
| ~ spl22_141
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1604,f1542,f1277,f4152]) ).
fof(f1604,plain,
( ! [X18,X16,X17] :
( element(sK13(X16,X17,sK6(X18)),X17)
| sP2(X16,X17,sK6(X18))
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) )
| ~ spl22_141
| ~ spl22_168 ),
inference(resolution,[],[f1543,f1278]) ).
fof(f4150,plain,
( spl22_369
| ~ spl22_65
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1595,f1542,f610,f4148]) ).
fof(f1595,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,powerset(X1),X2),X2)
| sP2(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK13(X0,powerset(X1),X2)) )
| ~ spl22_65
| ~ spl22_168 ),
inference(resolution,[],[f1543,f611]) ).
fof(f4146,plain,
( spl22_368
| ~ spl22_141
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1584,f1533,f1277,f4144]) ).
fof(f1584,plain,
( ! [X16,X17,X15] :
( element(sK13(X15,sK6(X16),X17),X17)
| sP2(X15,sK6(X16),X17)
| element(sK13(X15,sK6(X16),X17),X16)
| empty(X16) )
| ~ spl22_141
| ~ spl22_166 ),
inference(resolution,[],[f1534,f1278]) ).
fof(f4141,plain,
( spl22_367
| ~ spl22_65
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1575,f1533,f610,f4139]) ).
fof(f1575,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,powerset(X2)),X1)
| sP2(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK13(X0,X1,powerset(X2))) )
| ~ spl22_65
| ~ spl22_166 ),
inference(resolution,[],[f1534,f611]) ).
fof(f4137,plain,
( spl22_366
| ~ spl22_76
| ~ spl22_144 ),
inference(avatar_split_clause,[],[f1330,f1308,f684,f4135]) ).
fof(f1308,plain,
( spl22_144
<=> ! [X2] :
( empty(powerset(X2))
| in(sK6(X2),powerset(X2))
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_144])]) ).
fof(f1330,plain,
( ! [X2,X1] :
( empty(powerset(X1))
| empty(X1)
| apply(relation_dom_restriction(X2,powerset(X1)),sK6(X1)) = apply(X2,sK6(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_76
| ~ spl22_144 ),
inference(resolution,[],[f1309,f685]) ).
fof(f1309,plain,
( ! [X2] :
( in(sK6(X2),powerset(X2))
| empty(powerset(X2))
| empty(X2) )
| ~ spl22_144 ),
inference(avatar_component_clause,[],[f1308]) ).
fof(f4133,plain,
( spl22_365
| ~ spl22_78
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1298,f1277,f692,f4131]) ).
fof(f1298,plain,
( ! [X16,X14,X15] :
( element(sK13(sK6(X14),X15,X16),X14)
| empty(X14)
| in(sK13(sK6(X14),X15,X16),X16)
| sP2(sK6(X14),X15,X16) )
| ~ spl22_78
| ~ spl22_141 ),
inference(resolution,[],[f1278,f693]) ).
fof(f4129,plain,
( spl22_364
| ~ spl22_77
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1297,f1277,f688,f4127]) ).
fof(f1297,plain,
( ! [X11,X12,X13] :
( element(sK13(X11,sK6(X12),X13),X12)
| empty(X12)
| in(sK13(X11,sK6(X12),X13),X13)
| sP2(X11,sK6(X12),X13) )
| ~ spl22_77
| ~ spl22_141 ),
inference(resolution,[],[f1278,f689]) ).
fof(f4125,plain,
( spl22_363
| ~ spl22_77
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1296,f1277,f688,f4123]) ).
fof(f1296,plain,
( ! [X10,X8,X9] :
( element(sK13(X8,X9,sK6(X10)),X10)
| empty(X10)
| in(sK13(X8,X9,sK6(X10)),X9)
| sP2(X8,X9,sK6(X10)) )
| ~ spl22_77
| ~ spl22_141 ),
inference(resolution,[],[f1278,f689]) ).
fof(f4121,plain,
( spl22_362
| ~ spl22_78
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1295,f1277,f692,f4119]) ).
fof(f1295,plain,
( ! [X6,X7,X5] :
( element(sK13(X5,X6,sK6(X7)),X7)
| empty(X7)
| in(sK13(X5,X6,sK6(X7)),X5)
| sP2(X5,X6,sK6(X7)) )
| ~ spl22_78
| ~ spl22_141 ),
inference(resolution,[],[f1278,f693]) ).
fof(f4053,plain,
( ~ spl22_361
| ~ spl22_45
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f3847,f3668,f448,f4050]) ).
fof(f4050,plain,
( spl22_361
<=> in(relation_dom(sK5),sK8(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_361])]) ).
fof(f3668,plain,
( spl22_339
<=> in(sK8(sK5,sK15),relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_339])]) ).
fof(f3847,plain,
( ~ in(relation_dom(sK5),sK8(sK5,sK15))
| ~ spl22_45
| ~ spl22_339 ),
inference(resolution,[],[f3669,f449]) ).
fof(f3669,plain,
( in(sK8(sK5,sK15),relation_dom(sK5))
| ~ spl22_339 ),
inference(avatar_component_clause,[],[f3668]) ).
fof(f4041,plain,
( spl22_360
| ~ spl22_67
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1521,f1489,f633,f4039]) ).
fof(f1521,plain,
( ! [X3,X4,X5] :
( in(sK8(X3,powerset(X4)),relation_dom(X3))
| sP0(X3,powerset(X4))
| element(X5,X4)
| ~ in(X5,sK7(X3,powerset(X4))) )
| ~ spl22_67
| ~ spl22_161 ),
inference(resolution,[],[f1490,f634]) ).
fof(f4037,plain,
( spl22_359
| ~ spl22_137
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1513,f1481,f1213,f4035]) ).
fof(f1513,plain,
( ! [X11,X12] :
( element(sK8(X11,sK10(powerset(X12))),relation_dom(X11))
| sP0(X11,sK10(powerset(X12)))
| element(sK7(X11,sK10(powerset(X12))),X12) )
| ~ spl22_137
| ~ spl22_159 ),
inference(resolution,[],[f1482,f1214]) ).
fof(f4033,plain,
( spl22_358
| ~ spl22_76
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1325,f1304,f684,f4031]) ).
fof(f1325,plain,
( ! [X2,X3,X4] :
( empty(powerset(X2))
| ~ subset(X3,X2)
| apply(relation_dom_restriction(X4,powerset(X2)),X3) = apply(X4,X3)
| ~ function(X4)
| ~ relation(X4) )
| ~ spl22_76
| ~ spl22_143 ),
inference(resolution,[],[f1305,f685]) ).
fof(f4029,plain,
( spl22_357
| ~ spl22_74
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1257,f1213,f668,f4027]) ).
fof(f1257,plain,
( ! [X2,X3] :
( element(sK7(X2,sK10(powerset(X3))),X3)
| in(sK8(X2,sK10(powerset(X3))),relation_dom(X2))
| sP0(X2,sK10(powerset(X3))) )
| ~ spl22_74
| ~ spl22_137 ),
inference(resolution,[],[f1214,f669]) ).
fof(f4025,plain,
( spl22_356
| ~ spl22_79
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1182,f1173,f718,f4023]) ).
fof(f1182,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK7(X1,sK10(powerset(X0))) = apply(X1,sK8(X1,sK10(powerset(X0))))
| sP0(X1,sK10(powerset(X0))) )
| ~ spl22_79
| ~ spl22_131 ),
inference(resolution,[],[f1174,f719]) ).
fof(f3933,plain,
( spl22_355
| ~ spl22_46
| ~ spl22_339 ),
inference(avatar_split_clause,[],[f3846,f3668,f452,f3930]) ).
fof(f3930,plain,
( spl22_355
<=> element(sK8(sK5,sK15),relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_355])]) ).
fof(f3846,plain,
( element(sK8(sK5,sK15),relation_dom(sK5))
| ~ spl22_46
| ~ spl22_339 ),
inference(resolution,[],[f3669,f453]) ).
fof(f3875,plain,
( spl22_354
| ~ spl22_52
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1627,f1558,f498,f3873]) ).
fof(f1627,plain,
( ! [X10,X8,X9] :
( in(sK13(powerset(X8),X9,X10),X10)
| sP2(powerset(X8),X9,X10)
| subset(sK13(powerset(X8),X9,X10),X8) )
| ~ spl22_52
| ~ spl22_172 ),
inference(resolution,[],[f1559,f499]) ).
fof(f3871,plain,
( spl22_353
| ~ spl22_52
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1612,f1550,f498,f3869]) ).
fof(f1612,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,X9,powerset(X10)),X8)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_170 ),
inference(resolution,[],[f1551,f499]) ).
fof(f3867,plain,
( spl22_352
| ~ spl22_52
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1597,f1542,f498,f3865]) ).
fof(f1597,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,powerset(X9),X10),X10)
| sP2(X8,powerset(X9),X10)
| subset(sK13(X8,powerset(X9),X10),X9) )
| ~ spl22_52
| ~ spl22_168 ),
inference(resolution,[],[f1543,f499]) ).
fof(f3863,plain,
( spl22_351
| ~ spl22_52
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1577,f1533,f498,f3861]) ).
fof(f1577,plain,
( ! [X10,X8,X9] :
( in(sK13(X8,X9,powerset(X10)),X9)
| sP2(X8,X9,powerset(X10))
| subset(sK13(X8,X9,powerset(X10)),X10) )
| ~ spl22_52
| ~ spl22_166 ),
inference(resolution,[],[f1534,f499]) ).
fof(f3859,plain,
( spl22_350
| ~ spl22_65
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1520,f1489,f610,f3857]) ).
fof(f1520,plain,
( ! [X2,X0,X1] :
( in(sK8(X0,powerset(X1)),relation_dom(X0))
| sP0(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK7(X0,powerset(X1))) )
| ~ spl22_65
| ~ spl22_161 ),
inference(resolution,[],[f1490,f611]) ).
fof(f3855,plain,
( spl22_349
| ~ spl22_141
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1512,f1481,f1277,f3853]) ).
fof(f1512,plain,
( ! [X10,X9] :
( element(sK8(X9,sK6(X10)),relation_dom(X9))
| sP0(X9,sK6(X10))
| element(sK7(X9,sK6(X10)),X10)
| empty(X10) )
| ~ spl22_141
| ~ spl22_159 ),
inference(resolution,[],[f1482,f1278]) ).
fof(f3851,plain,
( spl22_348
| ~ spl22_74
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1293,f1277,f668,f3849]) ).
fof(f1293,plain,
( ! [X2,X3] :
( element(sK7(X2,sK6(X3)),X3)
| empty(X3)
| in(sK8(X2,sK6(X3)),relation_dom(X2))
| sP0(X2,sK6(X3)) )
| ~ spl22_74
| ~ spl22_141 ),
inference(resolution,[],[f1278,f669]) ).
fof(f3833,plain,
( spl22_347
| ~ spl22_137
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1349,f1316,f1213,f3831]) ).
fof(f1349,plain,
( ! [X14,X13] :
( sP2(sK10(powerset(X13)),X14,sK10(powerset(X13)))
| element(sK13(sK10(powerset(X13)),X14,sK10(powerset(X13))),X13) )
| ~ spl22_137
| ~ spl22_146 ),
inference(resolution,[],[f1317,f1214]) ).
fof(f3829,plain,
( spl22_346
| ~ spl22_137
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1339,f1312,f1213,f3827]) ).
fof(f1339,plain,
( ! [X14,X13] :
( sP2(X13,sK10(powerset(X14)),sK10(powerset(X14)))
| element(sK13(X13,sK10(powerset(X14)),sK10(powerset(X14))),X14) )
| ~ spl22_137
| ~ spl22_145 ),
inference(resolution,[],[f1313,f1214]) ).
fof(f3765,plain,
( spl22_345
| ~ spl22_44
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1669,f1665,f444,f3763]) ).
fof(f1665,plain,
( spl22_178
<=> ! [X0,X1] :
( relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_178])]) ).
fof(f1669,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) )
| ~ spl22_44
| ~ spl22_178 ),
inference(duplicate_literal_removal,[],[f1668]) ).
fof(f1668,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ relation(X0) )
| ~ spl22_44
| ~ spl22_178 ),
inference(resolution,[],[f1666,f445]) ).
fof(f1666,plain,
( ! [X0,X1] :
( ~ relation(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1) )
| ~ spl22_178 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f3761,plain,
( ~ spl22_10
| spl22_239
| ~ spl22_150
| spl22_339 ),
inference(avatar_split_clause,[],[f3718,f3668,f1366,f2443,f264]) ).
fof(f2443,plain,
( spl22_239
<=> sP0(sK5,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_239])]) ).
fof(f3718,plain,
( sP0(sK5,sK15)
| ~ empty(sK15)
| ~ spl22_150
| spl22_339 ),
inference(resolution,[],[f3670,f1367]) ).
fof(f3670,plain,
( ~ in(sK8(sK5,sK15),relation_dom(sK5))
| spl22_339 ),
inference(avatar_component_clause,[],[f3668]) ).
fof(f3760,plain,
( spl22_344
| ~ spl22_62
| ~ spl22_164 ),
inference(avatar_split_clause,[],[f1527,f1502,f598,f3758]) ).
fof(f1502,plain,
( spl22_164
<=> ! [X8,X7] :
( sK7(X7,X8) = apply(X7,sK8(X7,X8))
| sP0(X7,X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_164])]) ).
fof(f1527,plain,
( ! [X6,X7] :
( sK7(X6,X7) = apply(X6,sK8(X6,X7))
| ~ empty(X7)
| relation_rng(X6) = X7
| ~ sP1(X6) )
| ~ spl22_62
| ~ spl22_164 ),
inference(resolution,[],[f1503,f599]) ).
fof(f1503,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| sK7(X7,X8) = apply(X7,sK8(X7,X8))
| ~ empty(X8) )
| ~ spl22_164 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f3756,plain,
( spl22_343
| ~ spl22_52
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1522,f1489,f498,f3754]) ).
fof(f1522,plain,
( ! [X6,X7] :
( in(sK8(X6,powerset(X7)),relation_dom(X6))
| sP0(X6,powerset(X7))
| subset(sK7(X6,powerset(X7)),X7) )
| ~ spl22_52
| ~ spl22_161 ),
inference(resolution,[],[f1490,f499]) ).
fof(f3752,plain,
( spl22_342
| ~ spl22_76
| ~ spl22_127 ),
inference(avatar_split_clause,[],[f1177,f1156,f684,f3750]) ).
fof(f1156,plain,
( spl22_127
<=> ! [X4] :
( in(sK15,powerset(X4))
| empty(powerset(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_127])]) ).
fof(f1177,plain,
( ! [X2,X1] :
( empty(powerset(X1))
| apply(relation_dom_restriction(X2,powerset(X1)),sK15) = apply(X2,sK15)
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_76
| ~ spl22_127 ),
inference(resolution,[],[f1157,f685]) ).
fof(f1157,plain,
( ! [X4] :
( in(sK15,powerset(X4))
| empty(powerset(X4)) )
| ~ spl22_127 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f3748,plain,
( spl22_341
| ~ spl22_76
| ~ spl22_124 ),
inference(avatar_split_clause,[],[f1137,f1103,f684,f3746]) ).
fof(f1137,plain,
( ! [X2,X1] :
( empty(X1)
| apply(relation_dom_restriction(X2,X1),sK10(X1)) = apply(X2,sK10(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_76
| ~ spl22_124 ),
inference(resolution,[],[f1104,f685]) ).
fof(f3674,plain,
( ~ spl22_339
| spl22_340
| ~ spl22_153
| ~ spl22_251 ),
inference(avatar_split_clause,[],[f2928,f2597,f1395,f3672,f3668]) ).
fof(f2597,plain,
( spl22_251
<=> sK7(sK5,sK15) = apply(sK5,sK8(sK5,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_251])]) ).
fof(f2928,plain,
( ! [X0] :
( in(sK7(sK5,sK15),X0)
| ~ in(sK8(sK5,sK15),relation_dom(sK5))
| ~ sP0(sK5,X0) )
| ~ spl22_153
| ~ spl22_251 ),
inference(superposition,[],[f1396,f2599]) ).
fof(f2599,plain,
( sK7(sK5,sK15) = apply(sK5,sK8(sK5,sK15))
| ~ spl22_251 ),
inference(avatar_component_clause,[],[f2597]) ).
fof(f3455,plain,
( spl22_338
| ~ spl22_51
| ~ spl22_174 ),
inference(avatar_split_clause,[],[f1642,f1566,f494,f3453]) ).
fof(f3453,plain,
( spl22_338
<=> ! [X2,X3] :
( relation_dom(X2) != set_intersection2(X3,relation_dom(X2))
| relation_dom_restriction(X2,X3) = X2
| ~ function(X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_338])]) ).
fof(f1642,plain,
( ! [X2,X3] :
( relation_dom(X2) != set_intersection2(X3,relation_dom(X2))
| relation_dom_restriction(X2,X3) = X2
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_51
| ~ spl22_174 ),
inference(superposition,[],[f1567,f495]) ).
fof(f3451,plain,
( spl22_337
| ~ spl22_131
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1636,f1558,f1173,f3449]) ).
fof(f1636,plain,
( ! [X24,X22,X23] :
( element(sK13(X22,X23,sK10(powerset(X24))),X22)
| sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X24) )
| ~ spl22_131
| ~ spl22_172 ),
inference(resolution,[],[f1559,f1174]) ).
fof(f3447,plain,
( spl22_336
| ~ spl22_45
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1633,f1558,f448,f3445]) ).
fof(f3445,plain,
( spl22_336
<=> ! [X13,X14,X15] :
( element(sK13(X13,X14,X15),X13)
| sP2(X13,X14,X15)
| ~ in(X15,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_336])]) ).
fof(f1633,plain,
( ! [X14,X15,X13] :
( element(sK13(X13,X14,X15),X13)
| sP2(X13,X14,X15)
| ~ in(X15,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_172 ),
inference(resolution,[],[f1559,f449]) ).
fof(f3443,plain,
( spl22_335
| ~ spl22_131
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1621,f1550,f1173,f3441]) ).
fof(f1621,plain,
( ! [X21,X22,X23] :
( element(sK13(sK10(powerset(X21)),X22,X23),X23)
| sP2(sK10(powerset(X21)),X22,X23)
| ~ empty(X21) )
| ~ spl22_131
| ~ spl22_170 ),
inference(resolution,[],[f1551,f1174]) ).
fof(f3439,plain,
( spl22_334
| ~ spl22_45
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1618,f1550,f448,f3437]) ).
fof(f3437,plain,
( spl22_334
<=> ! [X13,X12,X14] :
( element(sK13(X12,X13,X14),X14)
| sP2(X12,X13,X14)
| ~ in(X12,sK13(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_334])]) ).
fof(f1618,plain,
( ! [X14,X12,X13] :
( element(sK13(X12,X13,X14),X14)
| sP2(X12,X13,X14)
| ~ in(X12,sK13(X12,X13,X14)) )
| ~ spl22_45
| ~ spl22_170 ),
inference(resolution,[],[f1551,f449]) ).
fof(f3435,plain,
( spl22_333
| ~ spl22_46
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1617,f1550,f452,f3433]) ).
fof(f1617,plain,
( ! [X10,X11,X9] :
( element(sK13(X9,X10,X11),X11)
| sP2(X9,X10,X11)
| element(sK13(X9,X10,X11),X9) )
| ~ spl22_46
| ~ spl22_170 ),
inference(resolution,[],[f1551,f453]) ).
fof(f3431,plain,
( spl22_332
| ~ spl22_131
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1606,f1542,f1173,f3429]) ).
fof(f1606,plain,
( ! [X24,X22,X23] :
( element(sK13(X22,X23,sK10(powerset(X24))),X23)
| sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X24) )
| ~ spl22_131
| ~ spl22_168 ),
inference(resolution,[],[f1543,f1174]) ).
fof(f3427,plain,
( spl22_331
| ~ spl22_45
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1603,f1542,f448,f3425]) ).
fof(f3425,plain,
( spl22_331
<=> ! [X13,X14,X15] :
( element(sK13(X13,X14,X15),X14)
| sP2(X13,X14,X15)
| ~ in(X15,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_331])]) ).
fof(f1603,plain,
( ! [X14,X15,X13] :
( element(sK13(X13,X14,X15),X14)
| sP2(X13,X14,X15)
| ~ in(X15,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_168 ),
inference(resolution,[],[f1543,f449]) ).
fof(f3423,plain,
( spl22_330
| ~ spl22_131
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1586,f1533,f1173,f3421]) ).
fof(f1586,plain,
( ! [X21,X22,X23] :
( element(sK13(X21,sK10(powerset(X22)),X23),X23)
| sP2(X21,sK10(powerset(X22)),X23)
| ~ empty(X22) )
| ~ spl22_131
| ~ spl22_166 ),
inference(resolution,[],[f1534,f1174]) ).
fof(f3402,plain,
( spl22_329
| ~ spl22_45
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1583,f1533,f448,f3400]) ).
fof(f3400,plain,
( spl22_329
<=> ! [X13,X12,X14] :
( element(sK13(X12,X13,X14),X14)
| sP2(X12,X13,X14)
| ~ in(X13,sK13(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_329])]) ).
fof(f1583,plain,
( ! [X14,X12,X13] :
( element(sK13(X12,X13,X14),X14)
| sP2(X12,X13,X14)
| ~ in(X13,sK13(X12,X13,X14)) )
| ~ spl22_45
| ~ spl22_166 ),
inference(resolution,[],[f1534,f449]) ).
fof(f3398,plain,
( spl22_328
| ~ spl22_46
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1582,f1533,f452,f3396]) ).
fof(f1582,plain,
( ! [X10,X11,X9] :
( element(sK13(X9,X10,X11),X11)
| sP2(X9,X10,X11)
| element(sK13(X9,X10,X11),X10) )
| ~ spl22_46
| ~ spl22_166 ),
inference(resolution,[],[f1534,f453]) ).
fof(f3394,plain,
( spl22_327
| ~ spl22_137
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1472,f1411,f1213,f3392]) ).
fof(f1472,plain,
( ! [X21,X19,X20] :
( sP2(X19,X20,sK10(powerset(X21)))
| ~ empty(X19)
| element(sK13(X19,X20,sK10(powerset(X21))),X21) )
| ~ spl22_137
| ~ spl22_157 ),
inference(resolution,[],[f1412,f1214]) ).
fof(f3390,plain,
( spl22_326
| ~ spl22_141
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1471,f1411,f1277,f3388]) ).
fof(f1471,plain,
( ! [X18,X16,X17] :
( sP2(X16,X17,sK6(X18))
| ~ empty(X16)
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) )
| ~ spl22_141
| ~ spl22_157 ),
inference(resolution,[],[f1412,f1278]) ).
fof(f3386,plain,
( spl22_325
| ~ spl22_137
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1462,f1407,f1213,f3384]) ).
fof(f1462,plain,
( ! [X18,X19,X20] :
( sP2(sK10(powerset(X18)),X19,X20)
| ~ empty(X20)
| element(sK13(sK10(powerset(X18)),X19,X20),X18) )
| ~ spl22_137
| ~ spl22_156 ),
inference(resolution,[],[f1408,f1214]) ).
fof(f3382,plain,
( spl22_324
| ~ spl22_141
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1461,f1407,f1277,f3380]) ).
fof(f1461,plain,
( ! [X16,X17,X15] :
( sP2(sK6(X15),X16,X17)
| ~ empty(X17)
| element(sK13(sK6(X15),X16,X17),X15)
| empty(X15) )
| ~ spl22_141
| ~ spl22_156 ),
inference(resolution,[],[f1408,f1278]) ).
fof(f3378,plain,
( spl22_323
| ~ spl22_137
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1452,f1403,f1213,f3376]) ).
fof(f1452,plain,
( ! [X21,X19,X20] :
( sP2(X19,X20,sK10(powerset(X21)))
| ~ empty(X20)
| element(sK13(X19,X20,sK10(powerset(X21))),X21) )
| ~ spl22_137
| ~ spl22_155 ),
inference(resolution,[],[f1404,f1214]) ).
fof(f3374,plain,
( spl22_322
| ~ spl22_141
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1451,f1403,f1277,f3372]) ).
fof(f1451,plain,
( ! [X18,X16,X17] :
( sP2(X16,X17,sK6(X18))
| ~ empty(X17)
| element(sK13(X16,X17,sK6(X18)),X18)
| empty(X18) )
| ~ spl22_141
| ~ spl22_155 ),
inference(resolution,[],[f1404,f1278]) ).
fof(f3370,plain,
( spl22_321
| ~ spl22_137
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1442,f1399,f1213,f3368]) ).
fof(f1442,plain,
( ! [X18,X19,X20] :
( sP2(X18,sK10(powerset(X19)),X20)
| ~ empty(X20)
| element(sK13(X18,sK10(powerset(X19)),X20),X19) )
| ~ spl22_137
| ~ spl22_154 ),
inference(resolution,[],[f1400,f1214]) ).
fof(f3366,plain,
( spl22_320
| ~ spl22_141
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1441,f1399,f1277,f3364]) ).
fof(f1441,plain,
( ! [X16,X17,X15] :
( sP2(X15,sK6(X16),X17)
| ~ empty(X17)
| element(sK13(X15,sK6(X16),X17),X16)
| empty(X16) )
| ~ spl22_141
| ~ spl22_154 ),
inference(resolution,[],[f1400,f1278]) ).
fof(f3345,plain,
( spl22_319
| ~ spl22_83
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1352,f1316,f740,f3343]) ).
fof(f1352,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(sK13(X0,X1,X0),X0)
| ~ in(sK13(X0,X1,X0),X1) )
| ~ spl22_83
| ~ spl22_146 ),
inference(duplicate_literal_removal,[],[f1343]) ).
fof(f1343,plain,
( ! [X0,X1] :
( sP2(X0,X1,X0)
| ~ in(sK13(X0,X1,X0),X0)
| ~ in(sK13(X0,X1,X0),X1)
| sP2(X0,X1,X0) )
| ~ spl22_83
| ~ spl22_146 ),
inference(resolution,[],[f1317,f741]) ).
fof(f3341,plain,
( spl22_318
| ~ spl22_141
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1348,f1316,f1277,f3339]) ).
fof(f1348,plain,
( ! [X11,X12] :
( sP2(sK6(X11),X12,sK6(X11))
| element(sK13(sK6(X11),X12,sK6(X11)),X11)
| empty(X11) )
| ~ spl22_141
| ~ spl22_146 ),
inference(resolution,[],[f1317,f1278]) ).
fof(f3337,plain,
( spl22_317
| ~ spl22_83
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1342,f1312,f740,f3335]) ).
fof(f1342,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(sK13(X0,X1,X1),X0)
| ~ in(sK13(X0,X1,X1),X1) )
| ~ spl22_83
| ~ spl22_145 ),
inference(duplicate_literal_removal,[],[f1333]) ).
fof(f1333,plain,
( ! [X0,X1] :
( sP2(X0,X1,X1)
| ~ in(sK13(X0,X1,X1),X0)
| ~ in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_83
| ~ spl22_145 ),
inference(resolution,[],[f1313,f741]) ).
fof(f3333,plain,
( spl22_316
| ~ spl22_141
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1338,f1312,f1277,f3331]) ).
fof(f1338,plain,
( ! [X11,X12] :
( sP2(X11,sK6(X12),sK6(X12))
| element(sK13(X11,sK6(X12),sK6(X12)),X12)
| empty(X12) )
| ~ spl22_141
| ~ spl22_145 ),
inference(resolution,[],[f1313,f1278]) ).
fof(f3329,plain,
( spl22_315
| ~ spl22_78
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1188,f1173,f692,f3327]) ).
fof(f1188,plain,
( ! [X16,X14,X15] :
( ~ empty(X14)
| in(sK13(sK10(powerset(X14)),X15,X16),X16)
| sP2(sK10(powerset(X14)),X15,X16) )
| ~ spl22_78
| ~ spl22_131 ),
inference(resolution,[],[f1174,f693]) ).
fof(f3325,plain,
( spl22_314
| ~ spl22_77
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1187,f1173,f688,f3323]) ).
fof(f1187,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| in(sK13(X12,sK10(powerset(X11)),X13),X13)
| sP2(X12,sK10(powerset(X11)),X13) )
| ~ spl22_77
| ~ spl22_131 ),
inference(resolution,[],[f1174,f689]) ).
fof(f3321,plain,
( spl22_313
| ~ spl22_77
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1186,f1173,f688,f3319]) ).
fof(f1186,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| in(sK13(X9,X10,sK10(powerset(X8))),X10)
| sP2(X9,X10,sK10(powerset(X8))) )
| ~ spl22_77
| ~ spl22_131 ),
inference(resolution,[],[f1174,f689]) ).
fof(f3317,plain,
( spl22_312
| ~ spl22_78
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1185,f1173,f692,f3315]) ).
fof(f1185,plain,
( ! [X6,X7,X5] :
( ~ empty(X5)
| in(sK13(X6,X7,sK10(powerset(X5))),X6)
| sP2(X6,X7,sK10(powerset(X5))) )
| ~ spl22_78
| ~ spl22_131 ),
inference(resolution,[],[f1174,f693]) ).
fof(f3295,plain,
( spl22_311
| ~ spl22_36
| ~ spl22_298 ),
inference(avatar_split_clause,[],[f3173,f3108,f393,f3293]) ).
fof(f3293,plain,
( spl22_311
<=> ! [X1] :
( sK7(sK5,relation_dom(X1)) = apply(sK5,sK8(sK5,relation_dom(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_311])]) ).
fof(f3108,plain,
( spl22_298
<=> ! [X1] :
( ~ empty(X1)
| sK7(sK5,X1) = apply(sK5,sK8(sK5,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_298])]) ).
fof(f3173,plain,
( ! [X1] :
( sK7(sK5,relation_dom(X1)) = apply(sK5,sK8(sK5,relation_dom(X1)))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_298 ),
inference(resolution,[],[f3109,f394]) ).
fof(f3109,plain,
( ! [X1] :
( ~ empty(X1)
| sK7(sK5,X1) = apply(sK5,sK8(sK5,X1)) )
| ~ spl22_298 ),
inference(avatar_component_clause,[],[f3108]) ).
fof(f3274,plain,
( spl22_310
| ~ spl22_131
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1514,f1481,f1173,f3272]) ).
fof(f1514,plain,
( ! [X14,X13] :
( element(sK8(X13,sK10(powerset(X14))),relation_dom(X13))
| sP0(X13,sK10(powerset(X14)))
| ~ empty(X14) )
| ~ spl22_131
| ~ spl22_159 ),
inference(resolution,[],[f1482,f1174]) ).
fof(f3270,plain,
( spl22_309
| ~ spl22_141
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1428,f1395,f1277,f3268]) ).
fof(f1428,plain,
( ! [X14,X15,X13] :
( ~ in(X13,relation_dom(X14))
| ~ sP0(X14,sK6(X15))
| element(apply(X14,X13),X15)
| empty(X15) )
| ~ spl22_141
| ~ spl22_153 ),
inference(resolution,[],[f1396,f1278]) ).
fof(f3266,plain,
( spl22_308
| ~ spl22_137
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1383,f1362,f1213,f3264]) ).
fof(f1383,plain,
( ! [X11,X12] :
( sP0(X11,sK10(powerset(X12)))
| ~ empty(relation_dom(X11))
| element(sK7(X11,sK10(powerset(X12))),X12) )
| ~ spl22_137
| ~ spl22_149 ),
inference(resolution,[],[f1363,f1214]) ).
fof(f3262,plain,
( spl22_307
| ~ spl22_141
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1382,f1362,f1277,f3260]) ).
fof(f1382,plain,
( ! [X10,X9] :
( sP0(X9,sK6(X10))
| ~ empty(relation_dom(X9))
| element(sK7(X9,sK6(X10)),X10)
| empty(X10) )
| ~ spl22_141
| ~ spl22_149 ),
inference(resolution,[],[f1363,f1278]) ).
fof(f3258,plain,
( spl22_306
| ~ spl22_74
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1183,f1173,f668,f3256]) ).
fof(f1183,plain,
( ! [X2,X3] :
( ~ empty(X2)
| in(sK8(X3,sK10(powerset(X2))),relation_dom(X3))
| sP0(X3,sK10(powerset(X2))) )
| ~ spl22_74
| ~ spl22_131 ),
inference(resolution,[],[f1174,f669]) ).
fof(f3252,plain,
( spl22_305
| ~ spl22_34
| ~ spl22_298 ),
inference(avatar_split_clause,[],[f3172,f3108,f385,f3250]) ).
fof(f3250,plain,
( spl22_305
<=> ! [X0] :
( sK7(sK5,relation_rng(X0)) = apply(sK5,sK8(sK5,relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_305])]) ).
fof(f3172,plain,
( ! [X0] :
( sK7(sK5,relation_rng(X0)) = apply(sK5,sK8(sK5,relation_rng(X0)))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_298 ),
inference(resolution,[],[f3109,f386]) ).
fof(f3239,plain,
( spl22_304
| ~ spl22_45
| ~ spl22_161 ),
inference(avatar_split_clause,[],[f1519,f1489,f448,f3237]) ).
fof(f1519,plain,
( ! [X8,X7] :
( element(sK7(X7,X8),X8)
| sP0(X7,X8)
| ~ in(relation_dom(X7),sK8(X7,X8)) )
| ~ spl22_45
| ~ spl22_161 ),
inference(resolution,[],[f1490,f449]) ).
fof(f3235,plain,
( spl22_303
| ~ spl22_45
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1511,f1481,f448,f3233]) ).
fof(f3233,plain,
( spl22_303
<=> ! [X7,X8] :
( element(sK8(X7,X8),relation_dom(X7))
| sP0(X7,X8)
| ~ in(X8,sK7(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_303])]) ).
fof(f1511,plain,
( ! [X8,X7] :
( element(sK8(X7,X8),relation_dom(X7))
| sP0(X7,X8)
| ~ in(X8,sK7(X7,X8)) )
| ~ spl22_45
| ~ spl22_159 ),
inference(resolution,[],[f1482,f449]) ).
fof(f3231,plain,
( spl22_302
| ~ spl22_46
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1510,f1481,f452,f3229]) ).
fof(f1510,plain,
( ! [X6,X5] :
( element(sK8(X5,X6),relation_dom(X5))
| sP0(X5,X6)
| element(sK7(X5,X6),X6) )
| ~ spl22_46
| ~ spl22_159 ),
inference(resolution,[],[f1482,f453]) ).
fof(f3227,plain,
( spl22_301
| ~ spl22_137
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1429,f1395,f1213,f3225]) ).
fof(f1429,plain,
( ! [X18,X16,X17] :
( ~ in(X16,relation_dom(X17))
| ~ sP0(X17,sK10(powerset(X18)))
| element(apply(X17,X16),X18) )
| ~ spl22_137
| ~ spl22_153 ),
inference(resolution,[],[f1396,f1214]) ).
fof(f3191,plain,
( spl22_300
| ~ spl22_31
| ~ spl22_94
| ~ spl22_174 ),
inference(avatar_split_clause,[],[f1646,f1566,f812,f373,f3189]) ).
fof(f3189,plain,
( spl22_300
<=> ! [X0] :
( relation_dom_restriction(X0,sK15) = X0
| relation_dom(X0) != sK15
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_300])]) ).
fof(f1646,plain,
( ! [X0] :
( relation_dom_restriction(X0,sK15) = X0
| relation_dom(X0) != sK15
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_31
| ~ spl22_94
| ~ spl22_174 ),
inference(forward_demodulation,[],[f1645,f814]) ).
fof(f1645,plain,
( ! [X0] :
( relation_dom(X0) != sK15
| relation_dom_restriction(X0,empty_set) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_31
| ~ spl22_94
| ~ spl22_174 ),
inference(forward_demodulation,[],[f1640,f814]) ).
fof(f1640,plain,
( ! [X0] :
( relation_dom(X0) != empty_set
| relation_dom_restriction(X0,empty_set) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_31
| ~ spl22_174 ),
inference(superposition,[],[f1567,f374]) ).
fof(f3187,plain,
( spl22_299
| ~ spl22_72
| ~ spl22_125 ),
inference(avatar_split_clause,[],[f1141,f1107,f660,f3185]) ).
fof(f1141,plain,
( ! [X0,X1] :
( ~ sP1(X0)
| ~ in(X1,relation_rng(X0))
| apply(X0,sK9(X0,X1)) = X1 )
| ~ spl22_72
| ~ spl22_125 ),
inference(resolution,[],[f1108,f661]) ).
fof(f3110,plain,
( spl22_298
| ~ spl22_164
| ~ spl22_258 ),
inference(avatar_split_clause,[],[f2769,f2723,f1502,f3108]) ).
fof(f2723,plain,
( spl22_258
<=> ! [X4] :
( ~ sP0(sK5,X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_258])]) ).
fof(f2769,plain,
( ! [X1] :
( ~ empty(X1)
| sK7(sK5,X1) = apply(sK5,sK8(sK5,X1)) )
| ~ spl22_164
| ~ spl22_258 ),
inference(duplicate_literal_removal,[],[f2768]) ).
fof(f2768,plain,
( ! [X1] :
( ~ empty(X1)
| sK7(sK5,X1) = apply(sK5,sK8(sK5,X1))
| ~ empty(X1) )
| ~ spl22_164
| ~ spl22_258 ),
inference(resolution,[],[f2724,f1503]) ).
fof(f2724,plain,
( ! [X4] :
( ~ sP0(sK5,X4)
| ~ empty(X4) )
| ~ spl22_258 ),
inference(avatar_component_clause,[],[f2723]) ).
fof(f3077,plain,
( spl22_297
| ~ spl22_58
| ~ spl22_158 ),
inference(avatar_split_clause,[],[f1506,f1477,f548,f3075]) ).
fof(f1477,plain,
( spl22_158
<=> ! [X2,X3] :
( ~ function(relation_dom_restriction(X2,X3))
| ~ empty(relation_dom_restriction(X2,X3))
| one_to_one(relation_dom_restriction(X2,X3))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_158])]) ).
fof(f1506,plain,
( ! [X0,X1] :
( ~ empty(relation_dom_restriction(X0,X1))
| one_to_one(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_158 ),
inference(duplicate_literal_removal,[],[f1505]) ).
fof(f1505,plain,
( ! [X0,X1] :
( ~ empty(relation_dom_restriction(X0,X1))
| one_to_one(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_158 ),
inference(resolution,[],[f1478,f549]) ).
fof(f1478,plain,
( ! [X2,X3] :
( ~ function(relation_dom_restriction(X2,X3))
| ~ empty(relation_dom_restriction(X2,X3))
| one_to_one(relation_dom_restriction(X2,X3))
| ~ relation(X2) )
| ~ spl22_158 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f3073,plain,
( spl22_296
| ~ spl22_45
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1470,f1411,f448,f3071]) ).
fof(f3071,plain,
( spl22_296
<=> ! [X13,X14,X15] :
( sP2(X13,X14,X15)
| ~ empty(X13)
| ~ in(X15,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_296])]) ).
fof(f1470,plain,
( ! [X14,X15,X13] :
( sP2(X13,X14,X15)
| ~ empty(X13)
| ~ in(X15,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_157 ),
inference(resolution,[],[f1412,f449]) ).
fof(f3069,plain,
( spl22_295
| ~ spl22_46
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1469,f1411,f452,f3067]) ).
fof(f1469,plain,
( ! [X10,X11,X12] :
( sP2(X10,X11,X12)
| ~ empty(X10)
| element(sK13(X10,X11,X12),X12) )
| ~ spl22_46
| ~ spl22_157 ),
inference(resolution,[],[f1412,f453]) ).
fof(f3065,plain,
( spl22_294
| ~ spl22_45
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1460,f1407,f448,f3063]) ).
fof(f3063,plain,
( spl22_294
<=> ! [X13,X12,X14] :
( sP2(X12,X13,X14)
| ~ empty(X14)
| ~ in(X12,sK13(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_294])]) ).
fof(f1460,plain,
( ! [X14,X12,X13] :
( sP2(X12,X13,X14)
| ~ empty(X14)
| ~ in(X12,sK13(X12,X13,X14)) )
| ~ spl22_45
| ~ spl22_156 ),
inference(resolution,[],[f1408,f449]) ).
fof(f3061,plain,
( spl22_293
| ~ spl22_46
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1459,f1407,f452,f3059]) ).
fof(f1459,plain,
( ! [X10,X11,X9] :
( sP2(X9,X10,X11)
| ~ empty(X11)
| element(sK13(X9,X10,X11),X9) )
| ~ spl22_46
| ~ spl22_156 ),
inference(resolution,[],[f1408,f453]) ).
fof(f3057,plain,
( spl22_292
| ~ spl22_45
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1450,f1403,f448,f3055]) ).
fof(f3055,plain,
( spl22_292
<=> ! [X13,X14,X15] :
( sP2(X13,X14,X15)
| ~ empty(X14)
| ~ in(X15,sK13(X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_292])]) ).
fof(f1450,plain,
( ! [X14,X15,X13] :
( sP2(X13,X14,X15)
| ~ empty(X14)
| ~ in(X15,sK13(X13,X14,X15)) )
| ~ spl22_45
| ~ spl22_155 ),
inference(resolution,[],[f1404,f449]) ).
fof(f3053,plain,
( spl22_291
| ~ spl22_46
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1449,f1403,f452,f3051]) ).
fof(f1449,plain,
( ! [X10,X11,X12] :
( sP2(X10,X11,X12)
| ~ empty(X11)
| element(sK13(X10,X11,X12),X12) )
| ~ spl22_46
| ~ spl22_155 ),
inference(resolution,[],[f1404,f453]) ).
fof(f3037,plain,
( spl22_290
| ~ spl22_45
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1440,f1399,f448,f3035]) ).
fof(f3035,plain,
( spl22_290
<=> ! [X13,X12,X14] :
( sP2(X12,X13,X14)
| ~ empty(X14)
| ~ in(X13,sK13(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_290])]) ).
fof(f1440,plain,
( ! [X14,X12,X13] :
( sP2(X12,X13,X14)
| ~ empty(X14)
| ~ in(X13,sK13(X12,X13,X14)) )
| ~ spl22_45
| ~ spl22_154 ),
inference(resolution,[],[f1400,f449]) ).
fof(f3033,plain,
( spl22_289
| ~ spl22_46
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1439,f1399,f452,f3031]) ).
fof(f1439,plain,
( ! [X10,X11,X9] :
( sP2(X9,X10,X11)
| ~ empty(X11)
| element(sK13(X9,X10,X11),X10) )
| ~ spl22_46
| ~ spl22_154 ),
inference(resolution,[],[f1400,f453]) ).
fof(f3029,plain,
( spl22_288
| ~ spl22_45
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1427,f1395,f448,f3027]) ).
fof(f1427,plain,
( ! [X10,X11,X12] :
( ~ in(X10,relation_dom(X11))
| ~ sP0(X11,X12)
| ~ in(X12,apply(X11,X10)) )
| ~ spl22_45
| ~ spl22_153 ),
inference(resolution,[],[f1396,f449]) ).
fof(f3025,plain,
( spl22_287
| ~ spl22_46
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1426,f1395,f452,f3023]) ).
fof(f1426,plain,
( ! [X8,X9,X7] :
( ~ in(X7,relation_dom(X8))
| ~ sP0(X8,X9)
| element(apply(X8,X7),X9) )
| ~ spl22_46
| ~ spl22_153 ),
inference(resolution,[],[f1396,f453]) ).
fof(f3021,plain,
( spl22_286
| ~ spl22_71
| ~ spl22_125 ),
inference(avatar_split_clause,[],[f1142,f1107,f656,f3019]) ).
fof(f1142,plain,
( ! [X2,X3] :
( ~ sP1(X2)
| ~ in(X3,relation_rng(X2))
| in(sK9(X2,X3),relation_dom(X2)) )
| ~ spl22_71
| ~ spl22_125 ),
inference(resolution,[],[f1108,f657]) ).
fof(f3017,plain,
( spl22_285
| ~ spl22_79
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1047,f959,f718,f3015]) ).
fof(f1047,plain,
( ! [X0] :
( sK7(X0,sK15) = apply(X0,sK8(X0,sK15))
| sP0(X0,sK15) )
| ~ spl22_79
| ~ spl22_116 ),
inference(resolution,[],[f960,f719]) ).
fof(f3005,plain,
( spl22_284
| ~ spl22_2
| ~ spl22_1
| ~ spl22_276 ),
inference(avatar_split_clause,[],[f2940,f2799,f219,f224,f3002]) ).
fof(f2940,plain,
( ~ function(sK5)
| sK5 = relation_dom_restriction(sK5,relation_dom(sK5))
| ~ spl22_1
| ~ spl22_276 ),
inference(resolution,[],[f2800,f221]) ).
fof(f2981,plain,
( spl22_283
| ~ spl22_131
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1430,f1395,f1173,f2979]) ).
fof(f1430,plain,
( ! [X21,X19,X20] :
( ~ in(X19,relation_dom(X20))
| ~ sP0(X20,sK10(powerset(X21)))
| ~ empty(X21) )
| ~ spl22_131
| ~ spl22_153 ),
inference(resolution,[],[f1396,f1174]) ).
fof(f2977,plain,
( spl22_282
| ~ spl22_45
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1389,f1366,f448,f2975]) ).
fof(f2975,plain,
( spl22_282
<=> ! [X8,X7] :
( sP0(X7,X8)
| ~ empty(X8)
| ~ in(relation_dom(X7),sK8(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_282])]) ).
fof(f1389,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| ~ empty(X8)
| ~ in(relation_dom(X7),sK8(X7,X8)) )
| ~ spl22_45
| ~ spl22_150 ),
inference(resolution,[],[f1367,f449]) ).
fof(f2973,plain,
( spl22_281
| ~ spl22_46
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1388,f1366,f452,f2971]) ).
fof(f2971,plain,
( spl22_281
<=> ! [X6,X5] :
( sP0(X5,X6)
| ~ empty(X6)
| element(sK8(X5,X6),relation_dom(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_281])]) ).
fof(f1388,plain,
( ! [X6,X5] :
( sP0(X5,X6)
| ~ empty(X6)
| element(sK8(X5,X6),relation_dom(X5)) )
| ~ spl22_46
| ~ spl22_150 ),
inference(resolution,[],[f1367,f453]) ).
fof(f2969,plain,
( spl22_280
| ~ spl22_45
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1381,f1362,f448,f2967]) ).
fof(f1381,plain,
( ! [X8,X7] :
( sP0(X7,X8)
| ~ empty(relation_dom(X7))
| ~ in(X8,sK7(X7,X8)) )
| ~ spl22_45
| ~ spl22_149 ),
inference(resolution,[],[f1363,f449]) ).
fof(f2965,plain,
( spl22_279
| ~ spl22_46
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1380,f1362,f452,f2963]) ).
fof(f1380,plain,
( ! [X6,X5] :
( sP0(X5,X6)
| ~ empty(relation_dom(X5))
| element(sK7(X5,X6),X6) )
| ~ spl22_46
| ~ spl22_149 ),
inference(resolution,[],[f1363,f453]) ).
fof(f2961,plain,
( spl22_278
| ~ spl22_73
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1145,f1111,f664,f2959]) ).
fof(f664,plain,
( spl22_73
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_73])]) ).
fof(f1111,plain,
( spl22_126
<=> ! [X0,X1] : sP2(X0,X1,set_intersection2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_126])]) ).
fof(f1145,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) )
| ~ spl22_73
| ~ spl22_126 ),
inference(resolution,[],[f1112,f665]) ).
fof(f665,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl22_73 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f1112,plain,
( ! [X0,X1] : sP2(X0,X1,set_intersection2(X1,X0))
| ~ spl22_126 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f2836,plain,
( ~ spl22_87
| ~ spl22_277
| ~ spl22_125
| ~ spl22_258 ),
inference(avatar_split_clause,[],[f2766,f2723,f1107,f2833,f773]) ).
fof(f773,plain,
( spl22_87
<=> sP1(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_87])]) ).
fof(f2833,plain,
( spl22_277
<=> empty(relation_rng(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_277])]) ).
fof(f2766,plain,
( ~ empty(relation_rng(sK5))
| ~ sP1(sK5)
| ~ spl22_125
| ~ spl22_258 ),
inference(resolution,[],[f2724,f1108]) ).
fof(f2801,plain,
( spl22_276
| ~ spl22_40
| ~ spl22_174 ),
inference(avatar_split_clause,[],[f1644,f1566,f410,f2799]) ).
fof(f410,plain,
( spl22_40
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_40])]) ).
fof(f1644,plain,
( ! [X1] :
( relation_dom_restriction(X1,relation_dom(X1)) = X1
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_40
| ~ spl22_174 ),
inference(trivial_inequality_removal,[],[f1641]) ).
fof(f1641,plain,
( ! [X1] :
( relation_dom(X1) != relation_dom(X1)
| relation_dom_restriction(X1,relation_dom(X1)) = X1
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_40
| ~ spl22_174 ),
inference(superposition,[],[f1567,f411]) ).
fof(f411,plain,
( ! [X0] : set_intersection2(X0,X0) = X0
| ~ spl22_40 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f2797,plain,
( spl22_275
| ~ spl22_116
| ~ spl22_172 ),
inference(avatar_split_clause,[],[f1637,f1558,f959,f2795]) ).
fof(f1637,plain,
( ! [X26,X25] :
( element(sK13(X25,X26,sK15),X25)
| sP2(X25,X26,sK15) )
| ~ spl22_116
| ~ spl22_172 ),
inference(resolution,[],[f1559,f960]) ).
fof(f2793,plain,
( spl22_274
| ~ spl22_116
| ~ spl22_170 ),
inference(avatar_split_clause,[],[f1622,f1550,f959,f2791]) ).
fof(f1622,plain,
( ! [X24,X25] :
( element(sK13(sK15,X24,X25),X25)
| sP2(sK15,X24,X25) )
| ~ spl22_116
| ~ spl22_170 ),
inference(resolution,[],[f1551,f960]) ).
fof(f2789,plain,
( spl22_273
| ~ spl22_116
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1607,f1542,f959,f2787]) ).
fof(f1607,plain,
( ! [X26,X25] :
( element(sK13(X25,X26,sK15),X26)
| sP2(X25,X26,sK15) )
| ~ spl22_116
| ~ spl22_168 ),
inference(resolution,[],[f1543,f960]) ).
fof(f2785,plain,
( spl22_272
| ~ spl22_116
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f1587,f1533,f959,f2783]) ).
fof(f1587,plain,
( ! [X24,X25] :
( element(sK13(X24,sK15,X25),X25)
| sP2(X24,sK15,X25) )
| ~ spl22_116
| ~ spl22_166 ),
inference(resolution,[],[f1534,f960]) ).
fof(f2781,plain,
( spl22_271
| ~ spl22_131
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1473,f1411,f1173,f2779]) ).
fof(f1473,plain,
( ! [X24,X22,X23] :
( sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X22)
| ~ empty(X24) )
| ~ spl22_131
| ~ spl22_157 ),
inference(resolution,[],[f1412,f1174]) ).
fof(f2777,plain,
( spl22_270
| ~ spl22_131
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1463,f1407,f1173,f2775]) ).
fof(f1463,plain,
( ! [X21,X22,X23] :
( sP2(sK10(powerset(X21)),X22,X23)
| ~ empty(X23)
| ~ empty(X21) )
| ~ spl22_131
| ~ spl22_156 ),
inference(resolution,[],[f1408,f1174]) ).
fof(f2773,plain,
( spl22_269
| ~ spl22_131
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1453,f1403,f1173,f2771]) ).
fof(f1453,plain,
( ! [X24,X22,X23] :
( sP2(X22,X23,sK10(powerset(X24)))
| ~ empty(X23)
| ~ empty(X24) )
| ~ spl22_131
| ~ spl22_155 ),
inference(resolution,[],[f1404,f1174]) ).
fof(f2765,plain,
( spl22_268
| ~ spl22_131
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1443,f1399,f1173,f2763]) ).
fof(f1443,plain,
( ! [X21,X22,X23] :
( sP2(X21,sK10(powerset(X22)),X23)
| ~ empty(X23)
| ~ empty(X22) )
| ~ spl22_131
| ~ spl22_154 ),
inference(resolution,[],[f1400,f1174]) ).
fof(f2761,plain,
( spl22_267
| ~ spl22_131
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1384,f1362,f1173,f2759]) ).
fof(f1384,plain,
( ! [X14,X13] :
( sP0(X13,sK10(powerset(X14)))
| ~ empty(relation_dom(X13))
| ~ empty(X14) )
| ~ spl22_131
| ~ spl22_149 ),
inference(resolution,[],[f1363,f1174]) ).
fof(f2757,plain,
( spl22_266
| ~ spl22_131
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1350,f1316,f1173,f2755]) ).
fof(f1350,plain,
( ! [X16,X15] :
( sP2(sK10(powerset(X15)),X16,sK10(powerset(X15)))
| ~ empty(X15) )
| ~ spl22_131
| ~ spl22_146 ),
inference(resolution,[],[f1317,f1174]) ).
fof(f2753,plain,
( spl22_265
| ~ spl22_45
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1347,f1316,f448,f2751]) ).
fof(f1347,plain,
( ! [X10,X9] :
( sP2(X9,X10,X9)
| ~ in(X9,sK13(X9,X10,X9)) )
| ~ spl22_45
| ~ spl22_146 ),
inference(resolution,[],[f1317,f449]) ).
fof(f2749,plain,
( spl22_264
| ~ spl22_46
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1346,f1316,f452,f2747]) ).
fof(f1346,plain,
( ! [X8,X7] :
( sP2(X7,X8,X7)
| element(sK13(X7,X8,X7),X7) )
| ~ spl22_46
| ~ spl22_146 ),
inference(resolution,[],[f1317,f453]) ).
fof(f2745,plain,
( spl22_263
| ~ spl22_131
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1340,f1312,f1173,f2743]) ).
fof(f1340,plain,
( ! [X16,X15] :
( sP2(X15,sK10(powerset(X16)),sK10(powerset(X16)))
| ~ empty(X16) )
| ~ spl22_131
| ~ spl22_145 ),
inference(resolution,[],[f1313,f1174]) ).
fof(f2741,plain,
( spl22_262
| ~ spl22_45
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1337,f1312,f448,f2739]) ).
fof(f1337,plain,
( ! [X10,X9] :
( sP2(X9,X10,X10)
| ~ in(X10,sK13(X9,X10,X10)) )
| ~ spl22_45
| ~ spl22_145 ),
inference(resolution,[],[f1313,f449]) ).
fof(f2737,plain,
( spl22_261
| ~ spl22_46
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1336,f1312,f452,f2735]) ).
fof(f1336,plain,
( ! [X8,X7] :
( sP2(X7,X8,X8)
| element(sK13(X7,X8,X8),X8) )
| ~ spl22_46
| ~ spl22_145 ),
inference(resolution,[],[f1313,f453]) ).
fof(f2733,plain,
( spl22_260
| ~ spl22_45
| ~ spl22_144 ),
inference(avatar_split_clause,[],[f1332,f1308,f448,f2731]) ).
fof(f2731,plain,
( spl22_260
<=> ! [X4] :
( empty(powerset(X4))
| empty(X4)
| ~ in(powerset(X4),sK6(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_260])]) ).
fof(f1332,plain,
( ! [X4] :
( empty(powerset(X4))
| empty(X4)
| ~ in(powerset(X4),sK6(X4)) )
| ~ spl22_45
| ~ spl22_144 ),
inference(resolution,[],[f1309,f449]) ).
fof(f2729,plain,
( spl22_259
| ~ spl22_45
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1327,f1304,f448,f2727]) ).
fof(f1327,plain,
( ! [X8,X7] :
( empty(powerset(X7))
| ~ subset(X8,X7)
| ~ in(powerset(X7),X8) )
| ~ spl22_45
| ~ spl22_143 ),
inference(resolution,[],[f1305,f449]) ).
fof(f2725,plain,
( spl22_258
| ~ spl22_4
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2668,f2571,f234,f2723]) ).
fof(f2668,plain,
( ! [X4] :
( ~ sP0(sK5,X4)
| ~ empty(X4) )
| ~ spl22_4
| ~ spl22_250 ),
inference(resolution,[],[f2572,f236]) ).
fof(f2721,plain,
( spl22_257
| ~ spl22_124
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1294,f1277,f1103,f2719]) ).
fof(f1294,plain,
( ! [X4] :
( element(sK10(sK6(X4)),X4)
| empty(X4)
| empty(sK6(X4)) )
| ~ spl22_124
| ~ spl22_141 ),
inference(resolution,[],[f1278,f1104]) ).
fof(f2717,plain,
( spl22_256
| ~ spl22_124
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1258,f1213,f1103,f2715]) ).
fof(f1258,plain,
( ! [X4] :
( element(sK10(sK10(powerset(X4))),X4)
| empty(sK10(powerset(X4))) )
| ~ spl22_124
| ~ spl22_137 ),
inference(resolution,[],[f1214,f1104]) ).
fof(f2713,plain,
( spl22_255
| ~ spl22_78
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1052,f959,f692,f2711]) ).
fof(f1052,plain,
( ! [X8,X9] :
( in(sK13(sK15,X8,X9),X9)
| sP2(sK15,X8,X9) )
| ~ spl22_78
| ~ spl22_116 ),
inference(resolution,[],[f960,f693]) ).
fof(f2709,plain,
( spl22_254
| ~ spl22_77
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1051,f959,f688,f2707]) ).
fof(f1051,plain,
( ! [X6,X7] :
( in(sK13(X6,sK15,X7),X7)
| sP2(X6,sK15,X7) )
| ~ spl22_77
| ~ spl22_116 ),
inference(resolution,[],[f960,f689]) ).
fof(f2705,plain,
( spl22_253
| ~ spl22_77
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1050,f959,f688,f2703]) ).
fof(f1050,plain,
( ! [X4,X5] :
( in(sK13(X4,X5,sK15),X5)
| sP2(X4,X5,sK15) )
| ~ spl22_77
| ~ spl22_116 ),
inference(resolution,[],[f960,f689]) ).
fof(f2701,plain,
( spl22_252
| ~ spl22_78
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f1049,f959,f692,f2699]) ).
fof(f1049,plain,
( ! [X2,X3] :
( in(sK13(X2,X3,sK15),X2)
| sP2(X2,X3,sK15) )
| ~ spl22_78
| ~ spl22_116 ),
inference(resolution,[],[f960,f693]) ).
fof(f2600,plain,
( ~ spl22_10
| spl22_251
| ~ spl22_164
| spl22_239 ),
inference(avatar_split_clause,[],[f2539,f2443,f1502,f2597,f264]) ).
fof(f2539,plain,
( sK7(sK5,sK15) = apply(sK5,sK8(sK5,sK15))
| ~ empty(sK15)
| ~ spl22_164
| spl22_239 ),
inference(resolution,[],[f2445,f1503]) ).
fof(f2445,plain,
( ~ sP0(sK5,sK15)
| spl22_239 ),
inference(avatar_component_clause,[],[f2443]) ).
fof(f2573,plain,
( spl22_250
| ~ spl22_41
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1424,f1395,f414,f2571]) ).
fof(f1424,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP0(X1,X2)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_153 ),
inference(resolution,[],[f1396,f415]) ).
fof(f2569,plain,
( spl22_249
| ~ spl22_36
| ~ spl22_135 ),
inference(avatar_split_clause,[],[f1237,f1205,f393,f2567]) ).
fof(f1237,plain,
( ! [X2,X3] :
( ~ empty(X2)
| relation_dom(relation_dom(X3)) = X2
| ~ empty(X3) )
| ~ spl22_36
| ~ spl22_135 ),
inference(resolution,[],[f1206,f394]) ).
fof(f2565,plain,
( spl22_248
| ~ spl22_34
| ~ spl22_135 ),
inference(avatar_split_clause,[],[f1236,f1205,f385,f2563]) ).
fof(f1236,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl22_34
| ~ spl22_135 ),
inference(resolution,[],[f1206,f386]) ).
fof(f2561,plain,
( spl22_247
| ~ spl22_36
| ~ spl22_134 ),
inference(avatar_split_clause,[],[f1221,f1198,f393,f2559]) ).
fof(f1221,plain,
( ! [X2,X3] :
( ~ empty(X2)
| relation_rng(relation_dom(X3)) = X2
| ~ empty(X3) )
| ~ spl22_36
| ~ spl22_134 ),
inference(resolution,[],[f1199,f394]) ).
fof(f2557,plain,
( spl22_246
| ~ spl22_34
| ~ spl22_134 ),
inference(avatar_split_clause,[],[f1220,f1198,f385,f2555]) ).
fof(f1220,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl22_34
| ~ spl22_134 ),
inference(resolution,[],[f1199,f386]) ).
fof(f2470,plain,
( spl22_245
| ~ spl22_41
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1457,f1407,f414,f2468]) ).
fof(f1457,plain,
( ! [X2,X3,X4] :
( sP2(X2,X3,X4)
| ~ empty(X4)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_156 ),
inference(resolution,[],[f1408,f415]) ).
fof(f2466,plain,
( spl22_244
| ~ spl22_41
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1437,f1399,f414,f2464]) ).
fof(f1437,plain,
( ! [X2,X3,X4] :
( sP2(X2,X3,X4)
| ~ empty(X4)
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_154 ),
inference(resolution,[],[f1400,f415]) ).
fof(f2462,plain,
( spl22_243
| ~ spl22_41
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1378,f1362,f414,f2460]) ).
fof(f1378,plain,
( ! [X0,X1] :
( sP0(X0,X1)
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl22_41
| ~ spl22_149 ),
inference(resolution,[],[f1363,f415]) ).
fof(f2458,plain,
( spl22_242
| ~ spl22_111
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1377,f1358,f940,f2456]) ).
fof(f1358,plain,
( spl22_148
<=> ! [X1] :
( ~ function(relation_dom(X1))
| ~ empty(relation_dom(X1))
| one_to_one(relation_dom(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_148])]) ).
fof(f1377,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_148 ),
inference(duplicate_literal_removal,[],[f1376]) ).
fof(f1376,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_148 ),
inference(resolution,[],[f1359,f941]) ).
fof(f1359,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| ~ empty(relation_dom(X1))
| one_to_one(relation_dom(X1))
| ~ empty(X1) )
| ~ spl22_148 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f2454,plain,
( spl22_241
| ~ spl22_110
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1370,f1354,f936,f2452]) ).
fof(f936,plain,
( spl22_110
<=> ! [X2] :
( ~ empty(X2)
| function(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_110])]) ).
fof(f1354,plain,
( spl22_147
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_147])]) ).
fof(f1370,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_147 ),
inference(duplicate_literal_removal,[],[f1369]) ).
fof(f1369,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_147 ),
inference(resolution,[],[f1355,f937]) ).
fof(f937,plain,
( ! [X2] :
( function(relation_rng(X2))
| ~ empty(X2) )
| ~ spl22_110 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f1355,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_147 ),
inference(avatar_component_clause,[],[f1354]) ).
fof(f2450,plain,
( spl22_240
| ~ spl22_58
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1323,f1300,f548,f2448]) ).
fof(f1300,plain,
( spl22_142
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| sP1(relation_dom_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_142])]) ).
fof(f1323,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1))
| ~ function(X0) )
| ~ spl22_58
| ~ spl22_142 ),
inference(duplicate_literal_removal,[],[f1322]) ).
fof(f1322,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_58
| ~ spl22_142 ),
inference(resolution,[],[f1301,f549]) ).
fof(f1301,plain,
( ! [X0,X1] :
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| sP1(relation_dom_restriction(X0,X1)) )
| ~ spl22_142 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f2446,plain,
( ~ spl22_239
| ~ spl22_4
| ~ spl22_236 ),
inference(avatar_split_clause,[],[f2404,f2331,f234,f2443]) ).
fof(f2404,plain,
( ~ sP0(sK5,sK15)
| ~ spl22_4
| ~ spl22_236 ),
inference(resolution,[],[f2332,f236]) ).
fof(f2441,plain,
( spl22_238
| ~ spl22_68
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1147,f1111,f637,f2439]) ).
fof(f637,plain,
( spl22_68
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_68])]) ).
fof(f1147,plain,
( ! [X8,X6,X7] :
( ~ in(X6,set_intersection2(X7,X8))
| in(X6,X7) )
| ~ spl22_68
| ~ spl22_126 ),
inference(resolution,[],[f1112,f638]) ).
fof(f638,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) )
| ~ spl22_68 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f2437,plain,
( spl22_237
| ~ spl22_69
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1146,f1111,f641,f2435]) ).
fof(f641,plain,
( spl22_69
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_69])]) ).
fof(f1146,plain,
( ! [X3,X4,X5] :
( ~ in(X3,set_intersection2(X4,X5))
| in(X3,X5) )
| ~ spl22_69
| ~ spl22_126 ),
inference(resolution,[],[f1112,f642]) ).
fof(f642,plain,
( ! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl22_69 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f2333,plain,
( spl22_236
| ~ spl22_116
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1431,f1395,f959,f2331]) ).
fof(f1431,plain,
( ! [X22,X23] :
( ~ in(X22,relation_dom(X23))
| ~ sP0(X23,sK15) )
| ~ spl22_116
| ~ spl22_153 ),
inference(resolution,[],[f1396,f960]) ).
fof(f2329,plain,
( spl22_235
| ~ spl22_36
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f1126,f1078,f393,f2327]) ).
fof(f1126,plain,
( ! [X1] :
( sK15 = relation_dom(relation_dom(X1))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_119 ),
inference(resolution,[],[f1079,f394]) ).
fof(f2308,plain,
( spl22_234
| ~ spl22_34
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f1125,f1078,f385,f2306]) ).
fof(f1125,plain,
( ! [X0] :
( sK15 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_119 ),
inference(resolution,[],[f1079,f386]) ).
fof(f2304,plain,
( spl22_233
| ~ spl22_36
| ~ spl22_118 ),
inference(avatar_split_clause,[],[f1115,f1074,f393,f2302]) ).
fof(f1115,plain,
( ! [X1] :
( sK15 = relation_rng(relation_dom(X1))
| ~ empty(X1) )
| ~ spl22_36
| ~ spl22_118 ),
inference(resolution,[],[f1075,f394]) ).
fof(f2300,plain,
( spl22_232
| ~ spl22_34
| ~ spl22_118 ),
inference(avatar_split_clause,[],[f1114,f1074,f385,f2298]) ).
fof(f1114,plain,
( ! [X0] :
( sK15 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_34
| ~ spl22_118 ),
inference(resolution,[],[f1075,f386]) ).
fof(f2296,plain,
( spl22_231
| ~ spl22_63
| ~ spl22_112 ),
inference(avatar_split_clause,[],[f1057,f944,f602,f2294]) ).
fof(f2294,plain,
( spl22_231
<=> ! [X0,X1] :
( sK15 != X1
| sP2(X0,sK15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_231])]) ).
fof(f602,plain,
( spl22_63
<=> ! [X2,X0,X1] :
( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_63])]) ).
fof(f1057,plain,
( ! [X0,X1] :
( sK15 != X1
| sP2(X0,sK15,X1) )
| ~ spl22_63
| ~ spl22_112 ),
inference(superposition,[],[f603,f945]) ).
fof(f603,plain,
( ! [X2,X0,X1] :
( set_intersection2(X0,X1) != X2
| sP2(X1,X0,X2) )
| ~ spl22_63 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f2288,plain,
( ~ spl22_2
| spl22_230
| ~ spl22_1
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1872,f1784,f219,f2286,f224]) ).
fof(f1872,plain,
( ! [X16,X17] :
( sP0(X16,X17)
| apply(relation_dom_restriction(sK5,X17),sK7(X16,X17)) = apply(sK5,sK7(X16,X17))
| ~ function(sK5)
| sK7(X16,X17) = apply(X16,sK8(X16,X17)) )
| ~ spl22_1
| ~ spl22_190 ),
inference(resolution,[],[f1785,f221]) ).
fof(f2273,plain,
( ~ spl22_2
| spl22_229
| ~ spl22_1
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1853,f1780,f219,f2271,f224]) ).
fof(f1853,plain,
( ! [X21,X22,X23] :
( sP2(X21,X22,X23)
| apply(sK5,sK13(X21,X22,X23)) = apply(relation_dom_restriction(sK5,X21),sK13(X21,X22,X23))
| ~ function(sK5)
| in(sK13(X21,X22,X23),X23) )
| ~ spl22_1
| ~ spl22_189 ),
inference(resolution,[],[f1781,f221]) ).
fof(f2258,plain,
( ~ spl22_2
| spl22_228
| ~ spl22_1
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1834,f1776,f219,f2256,f224]) ).
fof(f1834,plain,
( ! [X21,X22,X23] :
( sP2(X21,X22,X23)
| apply(relation_dom_restriction(sK5,X23),sK13(X21,X22,X23)) = apply(sK5,sK13(X21,X22,X23))
| ~ function(sK5)
| in(sK13(X21,X22,X23),X21) )
| ~ spl22_1
| ~ spl22_188 ),
inference(resolution,[],[f1777,f221]) ).
fof(f2254,plain,
( spl22_227
| ~ spl22_111
| ~ spl22_203 ),
inference(avatar_split_clause,[],[f2006,f1998,f940,f2252]) ).
fof(f2252,plain,
( spl22_227
<=> ! [X0] :
( apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_227])]) ).
fof(f1998,plain,
( spl22_203
<=> ! [X3] :
( ~ function(relation_dom(X3))
| apply(relation_dom(X3),sK4) = apply(relation_dom_restriction(relation_dom(X3),relation_dom(sK5)),sK4)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_203])]) ).
fof(f2006,plain,
( ! [X0] :
( apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_203 ),
inference(duplicate_literal_removal,[],[f2004]) ).
fof(f2004,plain,
( ! [X0] :
( apply(relation_dom(X0),sK4) = apply(relation_dom_restriction(relation_dom(X0),relation_dom(sK5)),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_203 ),
inference(resolution,[],[f1999,f941]) ).
fof(f1999,plain,
( ! [X3] :
( ~ function(relation_dom(X3))
| apply(relation_dom(X3),sK4) = apply(relation_dom_restriction(relation_dom(X3),relation_dom(sK5)),sK4)
| ~ empty(X3) )
| ~ spl22_203 ),
inference(avatar_component_clause,[],[f1998]) ).
fof(f2239,plain,
( ~ spl22_2
| spl22_226
| ~ spl22_1
| ~ spl22_187 ),
inference(avatar_split_clause,[],[f1815,f1772,f219,f2237,f224]) ).
fof(f1815,plain,
( ! [X21,X22,X23] :
( sP2(X21,X22,X23)
| apply(sK5,sK13(X21,X22,X23)) = apply(relation_dom_restriction(sK5,X22),sK13(X21,X22,X23))
| ~ function(sK5)
| in(sK13(X21,X22,X23),X23) )
| ~ spl22_1
| ~ spl22_187 ),
inference(resolution,[],[f1773,f221]) ).
fof(f2224,plain,
( ~ spl22_2
| spl22_225
| ~ spl22_1
| ~ spl22_186 ),
inference(avatar_split_clause,[],[f1796,f1768,f219,f2222,f224]) ).
fof(f1796,plain,
( ! [X21,X22,X23] :
( sP2(X21,X22,X23)
| apply(relation_dom_restriction(sK5,X23),sK13(X21,X22,X23)) = apply(sK5,sK13(X21,X22,X23))
| ~ function(sK5)
| in(sK13(X21,X22,X23),X22) )
| ~ spl22_1
| ~ spl22_186 ),
inference(resolution,[],[f1769,f221]) ).
fof(f2196,plain,
( spl22_224
| ~ spl22_110
| ~ spl22_202 ),
inference(avatar_split_clause,[],[f2003,f1994,f936,f2194]) ).
fof(f2194,plain,
( spl22_224
<=> ! [X0] :
( apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_224])]) ).
fof(f1994,plain,
( spl22_202
<=> ! [X2] :
( ~ function(relation_rng(X2))
| apply(relation_rng(X2),sK4) = apply(relation_dom_restriction(relation_rng(X2),relation_dom(sK5)),sK4)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_202])]) ).
fof(f2003,plain,
( ! [X0] :
( apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_202 ),
inference(duplicate_literal_removal,[],[f2001]) ).
fof(f2001,plain,
( ! [X0] :
( apply(relation_rng(X0),sK4) = apply(relation_dom_restriction(relation_rng(X0),relation_dom(sK5)),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_202 ),
inference(resolution,[],[f1995,f937]) ).
fof(f1995,plain,
( ! [X2] :
( ~ function(relation_rng(X2))
| apply(relation_rng(X2),sK4) = apply(relation_dom_restriction(relation_rng(X2),relation_dom(sK5)),sK4)
| ~ empty(X2) )
| ~ spl22_202 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f2166,plain,
( spl22_223
| ~ spl22_116
| ~ spl22_157 ),
inference(avatar_split_clause,[],[f1474,f1411,f959,f2164]) ).
fof(f1474,plain,
( ! [X26,X25] :
( sP2(X25,X26,sK15)
| ~ empty(X25) )
| ~ spl22_116
| ~ spl22_157 ),
inference(resolution,[],[f1412,f960]) ).
fof(f2162,plain,
( spl22_222
| ~ spl22_116
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1464,f1407,f959,f2160]) ).
fof(f2160,plain,
( spl22_222
<=> ! [X25,X24] :
( sP2(sK15,X24,X25)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_222])]) ).
fof(f1464,plain,
( ! [X24,X25] :
( sP2(sK15,X24,X25)
| ~ empty(X25) )
| ~ spl22_116
| ~ spl22_156 ),
inference(resolution,[],[f1408,f960]) ).
fof(f2158,plain,
( spl22_221
| ~ spl22_116
| ~ spl22_155 ),
inference(avatar_split_clause,[],[f1454,f1403,f959,f2156]) ).
fof(f1454,plain,
( ! [X26,X25] :
( sP2(X25,X26,sK15)
| ~ empty(X26) )
| ~ spl22_116
| ~ spl22_155 ),
inference(resolution,[],[f1404,f960]) ).
fof(f2154,plain,
( spl22_220
| ~ spl22_116
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1444,f1399,f959,f2152]) ).
fof(f2152,plain,
( spl22_220
<=> ! [X25,X24] :
( sP2(X24,sK15,X25)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_220])]) ).
fof(f1444,plain,
( ! [X24,X25] :
( sP2(X24,sK15,X25)
| ~ empty(X25) )
| ~ spl22_116
| ~ spl22_154 ),
inference(resolution,[],[f1400,f960]) ).
fof(f2150,plain,
( spl22_219
| ~ spl22_116
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1385,f1362,f959,f2148]) ).
fof(f1385,plain,
( ! [X15] :
( sP0(X15,sK15)
| ~ empty(relation_dom(X15)) )
| ~ spl22_116
| ~ spl22_149 ),
inference(resolution,[],[f1363,f960]) ).
fof(f2146,plain,
( spl22_218
| ~ spl22_41
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1344,f1316,f414,f2144]) ).
fof(f1344,plain,
( ! [X2,X3] :
( sP2(X2,X3,X2)
| ~ empty(X2) )
| ~ spl22_41
| ~ spl22_146 ),
inference(resolution,[],[f1317,f415]) ).
fof(f2126,plain,
( spl22_217
| ~ spl22_41
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1334,f1312,f414,f2124]) ).
fof(f1334,plain,
( ! [X2,X3] :
( sP2(X2,X3,X3)
| ~ empty(X3) )
| ~ spl22_41
| ~ spl22_145 ),
inference(resolution,[],[f1313,f415]) ).
fof(f2122,plain,
( spl22_216
| ~ spl22_124
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1184,f1173,f1103,f2120]) ).
fof(f1184,plain,
( ! [X4] :
( ~ empty(X4)
| empty(sK10(powerset(X4))) )
| ~ spl22_124
| ~ spl22_131 ),
inference(resolution,[],[f1174,f1104]) ).
fof(f2118,plain,
( spl22_215
| ~ spl22_51
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1151,f1111,f494,f2116]) ).
fof(f2116,plain,
( spl22_215
<=> ! [X2,X3] : sP2(X3,X2,set_intersection2(X3,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_215])]) ).
fof(f1151,plain,
( ! [X2,X3] : sP2(X3,X2,set_intersection2(X3,X2))
| ~ spl22_51
| ~ spl22_126 ),
inference(superposition,[],[f1112,f495]) ).
fof(f2114,plain,
( spl22_214
| ~ spl22_45
| ~ spl22_124 ),
inference(avatar_split_clause,[],[f1139,f1103,f448,f2112]) ).
fof(f1139,plain,
( ! [X4] :
( empty(X4)
| ~ in(X4,sK10(X4)) )
| ~ spl22_45
| ~ spl22_124 ),
inference(resolution,[],[f1104,f449]) ).
fof(f2104,plain,
( spl22_213
| ~ spl22_2
| ~ spl22_1
| ~ spl22_182 ),
inference(avatar_split_clause,[],[f1721,f1685,f219,f224,f2102]) ).
fof(f1721,plain,
( ! [X16,X17] :
( ~ function(sK5)
| apply(relation_dom_restriction(sK5,X16),sK7(X17,X16)) = apply(sK5,sK7(X17,X16))
| in(sK8(X17,X16),relation_dom(X17))
| sP0(X17,X16) )
| ~ spl22_1
| ~ spl22_182 ),
inference(resolution,[],[f1686,f221]) ).
fof(f2091,plain,
( spl22_212
| ~ spl22_2
| ~ spl22_1
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1702,f1681,f219,f224,f2089]) ).
fof(f1702,plain,
( ! [X16,X17] :
( ~ function(sK5)
| apply(relation_dom_restriction(sK5,relation_dom(X16)),sK8(X16,X17)) = apply(sK5,sK8(X16,X17))
| in(sK7(X16,X17),X17)
| sP0(X16,X17) )
| ~ spl22_1
| ~ spl22_181 ),
inference(resolution,[],[f1682,f221]) ).
fof(f2080,plain,
( spl22_211
| ~ spl22_59
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f872,f869,f552,f2078]) ).
fof(f2078,plain,
( spl22_211
<=> ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(set_intersection2(X0,X1),sK4) = apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_211])]) ).
fof(f869,plain,
( spl22_100
<=> ! [X1] :
( apply(relation_dom_restriction(X1,relation_dom(sK5)),sK4) = apply(X1,sK4)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_100])]) ).
fof(f872,plain,
( ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(set_intersection2(X0,X1),sK4) = apply(relation_dom_restriction(set_intersection2(X0,X1),relation_dom(sK5)),sK4)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_100 ),
inference(resolution,[],[f870,f553]) ).
fof(f870,plain,
( ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| apply(relation_dom_restriction(X1,relation_dom(sK5)),sK4) = apply(X1,sK4) )
| ~ spl22_100 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f2053,plain,
( spl22_210
| ~ spl22_59
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f849,f846,f552,f2051]) ).
fof(f2051,plain,
( spl22_210
<=> ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),sK3),sK4) = apply(set_intersection2(X0,X1),sK4)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_210])]) ).
fof(f846,plain,
( spl22_99
<=> ! [X0] :
( apply(relation_dom_restriction(X0,sK3),sK4) = apply(X0,sK4)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_99])]) ).
fof(f849,plain,
( ! [X0,X1] :
( ~ function(set_intersection2(X0,X1))
| apply(relation_dom_restriction(set_intersection2(X0,X1),sK3),sK4) = apply(set_intersection2(X0,X1),sK4)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl22_59
| ~ spl22_99 ),
inference(resolution,[],[f847,f553]) ).
fof(f847,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| apply(relation_dom_restriction(X0,sK3),sK4) = apply(X0,sK4) )
| ~ spl22_99 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f2034,plain,
( spl22_209
| ~ spl22_111
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1219,f1194,f940,f2032]) ).
fof(f1194,plain,
( spl22_133
<=> ! [X1] :
( ~ function(relation_dom(X1))
| sP1(relation_dom(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_133])]) ).
fof(f1219,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_133 ),
inference(duplicate_literal_removal,[],[f1218]) ).
fof(f1218,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_133 ),
inference(resolution,[],[f1195,f941]) ).
fof(f1195,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| sP1(relation_dom(X1))
| ~ empty(X1) )
| ~ spl22_133 ),
inference(avatar_component_clause,[],[f1194]) ).
fof(f2030,plain,
( spl22_208
| ~ spl22_110
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1217,f1190,f936,f2028]) ).
fof(f2028,plain,
( spl22_208
<=> ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_208])]) ).
fof(f1190,plain,
( spl22_132
<=> ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_132])]) ).
fof(f1217,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_132 ),
inference(duplicate_literal_removal,[],[f1216]) ).
fof(f1216,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_132 ),
inference(resolution,[],[f1191,f937]) ).
fof(f1191,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_132 ),
inference(avatar_component_clause,[],[f1190]) ).
fof(f2026,plain,
( spl22_207
| ~ spl22_31
| ~ spl22_94 ),
inference(avatar_split_clause,[],[f831,f812,f373,f2024]) ).
fof(f2024,plain,
( spl22_207
<=> ! [X0] : sK15 = set_intersection2(X0,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_207])]) ).
fof(f831,plain,
( ! [X0] : sK15 = set_intersection2(X0,sK15)
| ~ spl22_31
| ~ spl22_94 ),
inference(superposition,[],[f374,f814]) ).
fof(f2020,plain,
( spl22_206
| ~ spl22_44
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f875,f869,f444,f2018]) ).
fof(f875,plain,
( ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| apply(relation_dom_restriction(X4,X5),sK4) = apply(relation_dom_restriction(relation_dom_restriction(X4,X5),relation_dom(sK5)),sK4)
| ~ relation(X4) )
| ~ spl22_44
| ~ spl22_100 ),
inference(resolution,[],[f870,f445]) ).
fof(f2016,plain,
( spl22_205
| ~ spl22_111
| ~ spl22_194 ),
inference(avatar_split_clause,[],[f1915,f1909,f940,f2014]) ).
fof(f2014,plain,
( spl22_205
<=> ! [X0] :
( apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_205])]) ).
fof(f1909,plain,
( spl22_194
<=> ! [X3] :
( ~ function(relation_dom(X3))
| apply(relation_dom_restriction(relation_dom(X3),sK3),sK4) = apply(relation_dom(X3),sK4)
| ~ empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_194])]) ).
fof(f1915,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_194 ),
inference(duplicate_literal_removal,[],[f1914]) ).
fof(f1914,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_dom(X0),sK3),sK4) = apply(relation_dom(X0),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_111
| ~ spl22_194 ),
inference(resolution,[],[f1910,f941]) ).
fof(f1910,plain,
( ! [X3] :
( ~ function(relation_dom(X3))
| apply(relation_dom_restriction(relation_dom(X3),sK3),sK4) = apply(relation_dom(X3),sK4)
| ~ empty(X3) )
| ~ spl22_194 ),
inference(avatar_component_clause,[],[f1909]) ).
fof(f2010,plain,
( spl22_204
| ~ spl22_44
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f852,f846,f444,f2008]) ).
fof(f852,plain,
( ! [X4,X5] :
( ~ function(relation_dom_restriction(X4,X5))
| apply(relation_dom_restriction(relation_dom_restriction(X4,X5),sK3),sK4) = apply(relation_dom_restriction(X4,X5),sK4)
| ~ relation(X4) )
| ~ spl22_44
| ~ spl22_99 ),
inference(resolution,[],[f847,f445]) ).
fof(f2000,plain,
( spl22_203
| ~ spl22_37
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f874,f869,f397,f1998]) ).
fof(f874,plain,
( ! [X3] :
( ~ function(relation_dom(X3))
| apply(relation_dom(X3),sK4) = apply(relation_dom_restriction(relation_dom(X3),relation_dom(sK5)),sK4)
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_100 ),
inference(resolution,[],[f870,f398]) ).
fof(f1996,plain,
( spl22_202
| ~ spl22_35
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f873,f869,f389,f1994]) ).
fof(f873,plain,
( ! [X2] :
( ~ function(relation_rng(X2))
| apply(relation_rng(X2),sK4) = apply(relation_dom_restriction(relation_rng(X2),relation_dom(sK5)),sK4)
| ~ empty(X2) )
| ~ spl22_35
| ~ spl22_100 ),
inference(resolution,[],[f870,f390]) ).
fof(f1955,plain,
( spl22_201
| ~ spl22_110
| ~ spl22_193 ),
inference(avatar_split_clause,[],[f1913,f1905,f936,f1953]) ).
fof(f1953,plain,
( spl22_201
<=> ! [X0] :
( apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_201])]) ).
fof(f1905,plain,
( spl22_193
<=> ! [X2] :
( ~ function(relation_rng(X2))
| apply(relation_dom_restriction(relation_rng(X2),sK3),sK4) = apply(relation_rng(X2),sK4)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_193])]) ).
fof(f1913,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_193 ),
inference(duplicate_literal_removal,[],[f1912]) ).
fof(f1912,plain,
( ! [X0] :
( apply(relation_dom_restriction(relation_rng(X0),sK3),sK4) = apply(relation_rng(X0),sK4)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl22_110
| ~ spl22_193 ),
inference(resolution,[],[f1906,f937]) ).
fof(f1906,plain,
( ! [X2] :
( ~ function(relation_rng(X2))
| apply(relation_dom_restriction(relation_rng(X2),sK3),sK4) = apply(relation_rng(X2),sK4)
| ~ empty(X2) )
| ~ spl22_193 ),
inference(avatar_component_clause,[],[f1905]) ).
fof(f1941,plain,
( spl22_200
| ~ spl22_31
| ~ spl22_94
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1154,f1111,f812,f373,f1939]) ).
fof(f1939,plain,
( spl22_200
<=> ! [X0] : sP2(sK15,X0,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_200])]) ).
fof(f1154,plain,
( ! [X0] : sP2(sK15,X0,sK15)
| ~ spl22_31
| ~ spl22_94
| ~ spl22_126 ),
inference(forward_demodulation,[],[f1149,f814]) ).
fof(f1149,plain,
( ! [X0] : sP2(empty_set,X0,empty_set)
| ~ spl22_31
| ~ spl22_126 ),
inference(superposition,[],[f1112,f374]) ).
fof(f1937,plain,
( spl22_199
| ~ spl22_112
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1153,f1111,f944,f1935]) ).
fof(f1935,plain,
( spl22_199
<=> ! [X6] : sP2(X6,sK15,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_199])]) ).
fof(f1153,plain,
( ! [X6] : sP2(X6,sK15,sK15)
| ~ spl22_112
| ~ spl22_126 ),
inference(superposition,[],[f1112,f945]) ).
fof(f1933,plain,
( spl22_198
| ~ spl22_40
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1150,f1111,f410,f1931]) ).
fof(f1931,plain,
( spl22_198
<=> ! [X1] : sP2(X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_198])]) ).
fof(f1150,plain,
( ! [X1] : sP2(X1,X1,X1)
| ~ spl22_40
| ~ spl22_126 ),
inference(superposition,[],[f1112,f411]) ).
fof(f1929,plain,
( spl22_197
| ~ spl22_6
| ~ spl22_94
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f1132,f1078,f812,f244,f1926]) ).
fof(f244,plain,
( spl22_6
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).
fof(f1132,plain,
( sK15 = relation_dom(sK15)
| ~ spl22_6
| ~ spl22_94
| ~ spl22_119 ),
inference(forward_demodulation,[],[f1127,f814]) ).
fof(f1127,plain,
( sK15 = relation_dom(empty_set)
| ~ spl22_6
| ~ spl22_119 ),
inference(resolution,[],[f1079,f246]) ).
fof(f246,plain,
( empty(empty_set)
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f1924,plain,
( spl22_196
| ~ spl22_6
| ~ spl22_94
| ~ spl22_118 ),
inference(avatar_split_clause,[],[f1121,f1074,f812,f244,f1921]) ).
fof(f1121,plain,
( sK15 = relation_rng(sK15)
| ~ spl22_6
| ~ spl22_94
| ~ spl22_118 ),
inference(forward_demodulation,[],[f1116,f814]) ).
fof(f1116,plain,
( sK15 = relation_rng(empty_set)
| ~ spl22_6
| ~ spl22_118 ),
inference(resolution,[],[f1075,f246]) ).
fof(f1919,plain,
( spl22_195
| ~ spl22_39
| ~ spl22_109 ),
inference(avatar_split_clause,[],[f933,f930,f406,f1917]) ).
fof(f1917,plain,
( spl22_195
<=> ! [X0] : element(sK15,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_195])]) ).
fof(f406,plain,
( spl22_39
<=> ! [X0] : element(sK11(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_39])]) ).
fof(f930,plain,
( spl22_109
<=> ! [X0] : sK11(X0) = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_109])]) ).
fof(f933,plain,
( ! [X0] : element(sK15,powerset(X0))
| ~ spl22_39
| ~ spl22_109 ),
inference(superposition,[],[f407,f931]) ).
fof(f931,plain,
( ! [X0] : sK11(X0) = sK15
| ~ spl22_109 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f407,plain,
( ! [X0] : element(sK11(X0),powerset(X0))
| ~ spl22_39 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f1911,plain,
( spl22_194
| ~ spl22_37
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f851,f846,f397,f1909]) ).
fof(f851,plain,
( ! [X3] :
( ~ function(relation_dom(X3))
| apply(relation_dom_restriction(relation_dom(X3),sK3),sK4) = apply(relation_dom(X3),sK4)
| ~ empty(X3) )
| ~ spl22_37
| ~ spl22_99 ),
inference(resolution,[],[f847,f398]) ).
fof(f1907,plain,
( spl22_193
| ~ spl22_35
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f850,f846,f389,f1905]) ).
fof(f850,plain,
( ! [X2] :
( ~ function(relation_rng(X2))
| apply(relation_dom_restriction(relation_rng(X2),sK3),sK4) = apply(relation_rng(X2),sK4)
| ~ empty(X2) )
| ~ spl22_35
| ~ spl22_99 ),
inference(resolution,[],[f847,f390]) ).
fof(f1899,plain,
( ~ spl22_42
| spl22_192
| ~ spl22_7
| ~ spl22_94
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f886,f869,f812,f249,f1896,f433]) ).
fof(f886,plain,
( apply(sK15,sK4) = apply(relation_dom_restriction(sK15,relation_dom(sK5)),sK4)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_94
| ~ spl22_100 ),
inference(forward_demodulation,[],[f885,f814]) ).
fof(f885,plain,
( ~ function(sK15)
| apply(empty_set,sK4) = apply(relation_dom_restriction(empty_set,relation_dom(sK5)),sK4)
| ~ spl22_7
| ~ spl22_94
| ~ spl22_100 ),
inference(forward_demodulation,[],[f876,f814]) ).
fof(f876,plain,
( ~ function(empty_set)
| apply(empty_set,sK4) = apply(relation_dom_restriction(empty_set,relation_dom(sK5)),sK4)
| ~ spl22_7
| ~ spl22_100 ),
inference(resolution,[],[f870,f251]) ).
fof(f1890,plain,
( spl22_191
| ~ spl22_20
| ~ spl22_19
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f883,f869,f309,f314,f1887]) ).
fof(f883,plain,
( ~ function(sK20)
| apply(sK20,sK4) = apply(relation_dom_restriction(sK20,relation_dom(sK5)),sK4)
| ~ spl22_19
| ~ spl22_100 ),
inference(resolution,[],[f870,f311]) ).
fof(f1786,plain,
( spl22_190
| ~ spl22_76
| ~ spl22_79 ),
inference(avatar_split_clause,[],[f721,f718,f684,f1784]) ).
fof(f721,plain,
( ! [X2,X0,X1] :
( sK7(X0,X1) = apply(X0,sK8(X0,X1))
| sP0(X0,X1)
| apply(relation_dom_restriction(X2,X1),sK7(X0,X1)) = apply(X2,sK7(X0,X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ spl22_76
| ~ spl22_79 ),
inference(resolution,[],[f719,f685]) ).
fof(f1782,plain,
( spl22_189
| ~ spl22_76
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f712,f692,f684,f1780]) ).
fof(f712,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X0),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_76
| ~ spl22_78 ),
inference(resolution,[],[f693,f685]) ).
fof(f1778,plain,
( spl22_188
| ~ spl22_76
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f708,f692,f684,f1776]) ).
fof(f708,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X0)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_76
| ~ spl22_78 ),
inference(resolution,[],[f693,f685]) ).
fof(f1774,plain,
( spl22_187
| ~ spl22_76
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f703,f688,f684,f1772]) ).
fof(f703,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| sP2(X0,X1,X2)
| apply(X3,sK13(X0,X1,X2)) = apply(relation_dom_restriction(X3,X1),sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_76
| ~ spl22_77 ),
inference(resolution,[],[f689,f685]) ).
fof(f1770,plain,
( spl22_186
| ~ spl22_76
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f699,f688,f684,f1768]) ).
fof(f699,plain,
( ! [X2,X3,X0,X1] :
( in(sK13(X0,X1,X2),X1)
| sP2(X0,X1,X2)
| apply(relation_dom_restriction(X3,X2),sK13(X0,X1,X2)) = apply(X3,sK13(X0,X1,X2))
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_76
| ~ spl22_77 ),
inference(resolution,[],[f689,f685]) ).
fof(f1743,plain,
( spl22_185
| ~ spl22_84 ),
inference(avatar_split_clause,[],[f753,f750,f1741]) ).
fof(f750,plain,
( spl22_84
<=> ! [X4,X0,X2,X1] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_84])]) ).
fof(f753,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) )
| ~ spl22_84 ),
inference(equality_resolution,[],[f751]) ).
fof(f751,plain,
( ! [X2,X0,X1,X4] :
( relation_dom_restriction(X2,X0) != X1
| ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_84 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f1696,plain,
( spl22_184
| ~ spl22_18
| ~ spl22_17
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f882,f869,f299,f304,f1693]) ).
fof(f882,plain,
( ~ function(sK19)
| apply(sK19,sK4) = apply(relation_dom_restriction(sK19,relation_dom(sK5)),sK4)
| ~ spl22_17
| ~ spl22_100 ),
inference(resolution,[],[f870,f301]) ).
fof(f1691,plain,
( spl22_183
| ~ spl22_51
| ~ spl22_85 ),
inference(avatar_split_clause,[],[f760,f755,f494,f1689]) ).
fof(f1689,plain,
( spl22_183
<=> ! [X6,X4,X5] :
( set_intersection2(X5,relation_dom(X4)) != relation_dom(X6)
| in(sK12(X6,X4),relation_dom(X6))
| relation_dom_restriction(X4,X5) = X6
| ~ function(X4)
| ~ relation(X4)
| ~ function(X6)
| ~ relation(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_183])]) ).
fof(f760,plain,
( ! [X6,X4,X5] :
( set_intersection2(X5,relation_dom(X4)) != relation_dom(X6)
| in(sK12(X6,X4),relation_dom(X6))
| relation_dom_restriction(X4,X5) = X6
| ~ function(X4)
| ~ relation(X4)
| ~ function(X6)
| ~ relation(X6) )
| ~ spl22_51
| ~ spl22_85 ),
inference(superposition,[],[f756,f495]) ).
fof(f1687,plain,
( spl22_182
| ~ spl22_74
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f698,f684,f668,f1685]) ).
fof(f698,plain,
( ! [X6,X7,X5] :
( apply(relation_dom_restriction(X5,X6),sK7(X7,X6)) = apply(X5,sK7(X7,X6))
| ~ function(X5)
| ~ relation(X5)
| in(sK8(X7,X6),relation_dom(X7))
| sP0(X7,X6) )
| ~ spl22_74
| ~ spl22_76 ),
inference(resolution,[],[f685,f669]) ).
fof(f1683,plain,
( spl22_181
| ~ spl22_74
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f697,f684,f668,f1681]) ).
fof(f697,plain,
( ! [X2,X3,X4] :
( apply(relation_dom_restriction(X2,relation_dom(X3)),sK8(X3,X4)) = apply(X2,sK8(X3,X4))
| ~ function(X2)
| ~ relation(X2)
| in(sK7(X3,X4),X4)
| sP0(X3,X4) )
| ~ spl22_74
| ~ spl22_76 ),
inference(resolution,[],[f685,f669]) ).
fof(f1677,plain,
( spl22_180
| ~ spl22_40
| ~ spl22_85 ),
inference(avatar_split_clause,[],[f759,f755,f410,f1675]) ).
fof(f1675,plain,
( spl22_180
<=> ! [X2,X3] :
( relation_dom(X2) != relation_dom(X3)
| in(sK12(X3,X2),relation_dom(X3))
| relation_dom_restriction(X2,relation_dom(X2)) = X3
| ~ function(X2)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_180])]) ).
fof(f759,plain,
( ! [X2,X3] :
( relation_dom(X2) != relation_dom(X3)
| in(sK12(X3,X2),relation_dom(X3))
| relation_dom_restriction(X2,relation_dom(X2)) = X3
| ~ function(X2)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3) )
| ~ spl22_40
| ~ spl22_85 ),
inference(superposition,[],[f756,f411]) ).
fof(f1673,plain,
( spl22_179
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_85 ),
inference(avatar_split_clause,[],[f764,f755,f381,f373,f264,f1671]) ).
fof(f381,plain,
( spl22_33
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_33])]) ).
fof(f764,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,sK15) = X1
| relation_dom(X1) != sK15
| in(sK12(X1,X0),sK15)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_85 ),
inference(inner_rewriting,[],[f763]) ).
fof(f763,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,sK15) = X1
| relation_dom(X1) != sK15
| in(sK12(X1,X0),relation_dom(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_85 ),
inference(forward_demodulation,[],[f762,f419]) ).
fof(f419,plain,
( empty_set = sK15
| ~ spl22_10
| ~ spl22_33 ),
inference(resolution,[],[f382,f266]) ).
fof(f266,plain,
( empty(sK15)
| ~ spl22_10 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f382,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl22_33 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f762,plain,
( ! [X0,X1] :
( relation_dom(X1) != sK15
| in(sK12(X1,X0),relation_dom(X1))
| relation_dom_restriction(X0,empty_set) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_85 ),
inference(forward_demodulation,[],[f758,f419]) ).
fof(f758,plain,
( ! [X0,X1] :
( empty_set != relation_dom(X1)
| in(sK12(X1,X0),relation_dom(X1))
| relation_dom_restriction(X0,empty_set) = X1
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_31
| ~ spl22_85 ),
inference(superposition,[],[f756,f374]) ).
fof(f1667,plain,
( spl22_178
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f738,f735,f1665]) ).
fof(f735,plain,
( spl22_82
<=> ! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_82])]) ).
fof(f738,plain,
( ! [X0,X1] :
( relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) )
| ~ spl22_82 ),
inference(equality_resolution,[],[f736]) ).
fof(f736,plain,
( ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) != X1
| relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_82 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f1654,plain,
( spl22_177
| ~ spl22_45
| ~ spl22_79 ),
inference(avatar_split_clause,[],[f723,f718,f448,f1652]) ).
fof(f723,plain,
( ! [X6,X5] :
( sK7(X5,X6) = apply(X5,sK8(X5,X6))
| sP0(X5,X6)
| ~ in(X6,sK7(X5,X6)) )
| ~ spl22_45
| ~ spl22_79 ),
inference(resolution,[],[f719,f449]) ).
fof(f1650,plain,
( spl22_176
| ~ spl22_46
| ~ spl22_79 ),
inference(avatar_split_clause,[],[f722,f718,f452,f1648]) ).
fof(f722,plain,
( ! [X3,X4] :
( sK7(X3,X4) = apply(X3,sK8(X3,X4))
| sP0(X3,X4)
| element(sK7(X3,X4),X4) )
| ~ spl22_46
| ~ spl22_79 ),
inference(resolution,[],[f719,f453]) ).
fof(f1594,plain,
( spl22_175
| ~ spl22_2
| ~ spl22_1
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f877,f869,f219,f224,f1591]) ).
fof(f877,plain,
( ~ function(sK5)
| apply(sK5,sK4) = apply(relation_dom_restriction(sK5,relation_dom(sK5)),sK4)
| ~ spl22_1
| ~ spl22_100 ),
inference(resolution,[],[f870,f221]) ).
fof(f1568,plain,
( spl22_174
| ~ spl22_86 ),
inference(avatar_split_clause,[],[f770,f766,f1566]) ).
fof(f766,plain,
( spl22_86
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_86])]) ).
fof(f770,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_86 ),
inference(duplicate_literal_removal,[],[f769]) ).
fof(f769,plain,
( ! [X0,X1] :
( relation_dom_restriction(X0,X1) = X0
| relation_dom(X0) != set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_86 ),
inference(equality_resolution,[],[f767]) ).
fof(f767,plain,
( ! [X2,X0,X1] :
( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
| relation_dom_restriction(X2,X0) = X1
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_86 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f1564,plain,
( spl22_173
| ~ spl22_45
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f714,f692,f448,f1562]) ).
fof(f714,plain,
( ! [X8,X9,X7] :
( in(sK13(X7,X8,X9),X9)
| sP2(X7,X8,X9)
| ~ in(X7,sK13(X7,X8,X9)) )
| ~ spl22_45
| ~ spl22_78 ),
inference(resolution,[],[f693,f449]) ).
fof(f1560,plain,
( spl22_172
| ~ spl22_46
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f713,f692,f452,f1558]) ).
fof(f713,plain,
( ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X6)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X4) )
| ~ spl22_46
| ~ spl22_78 ),
inference(resolution,[],[f693,f453]) ).
fof(f1556,plain,
( spl22_171
| ~ spl22_45
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f710,f692,f448,f1554]) ).
fof(f710,plain,
( ! [X8,X9,X7] :
( in(sK13(X7,X8,X9),X7)
| sP2(X7,X8,X9)
| ~ in(X9,sK13(X7,X8,X9)) )
| ~ spl22_45
| ~ spl22_78 ),
inference(resolution,[],[f693,f449]) ).
fof(f1552,plain,
( spl22_170
| ~ spl22_46
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f709,f692,f452,f1550]) ).
fof(f709,plain,
( ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X4)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X6) )
| ~ spl22_46
| ~ spl22_78 ),
inference(resolution,[],[f693,f453]) ).
fof(f1548,plain,
( spl22_169
| ~ spl22_45
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f705,f688,f448,f1546]) ).
fof(f705,plain,
( ! [X8,X9,X7] :
( in(sK13(X7,X8,X9),X9)
| sP2(X7,X8,X9)
| ~ in(X8,sK13(X7,X8,X9)) )
| ~ spl22_45
| ~ spl22_77 ),
inference(resolution,[],[f689,f449]) ).
fof(f1544,plain,
( spl22_168
| ~ spl22_46
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f704,f688,f452,f1542]) ).
fof(f704,plain,
( ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X6)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X5) )
| ~ spl22_46
| ~ spl22_77 ),
inference(resolution,[],[f689,f453]) ).
fof(f1539,plain,
( spl22_167
| ~ spl22_45
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f701,f688,f448,f1537]) ).
fof(f701,plain,
( ! [X8,X9,X7] :
( in(sK13(X7,X8,X9),X8)
| sP2(X7,X8,X9)
| ~ in(X9,sK13(X7,X8,X9)) )
| ~ spl22_45
| ~ spl22_77 ),
inference(resolution,[],[f689,f449]) ).
fof(f1535,plain,
( spl22_166
| ~ spl22_46
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f700,f688,f452,f1533]) ).
fof(f700,plain,
( ! [X6,X4,X5] :
( in(sK13(X4,X5,X6),X5)
| sP2(X4,X5,X6)
| element(sK13(X4,X5,X6),X6) )
| ~ spl22_46
| ~ spl22_77 ),
inference(resolution,[],[f689,f453]) ).
fof(f1531,plain,
( spl22_165
| ~ spl22_55
| ~ spl22_59 ),
inference(avatar_split_clause,[],[f586,f552,f536,f1529]) ).
fof(f1529,plain,
( spl22_165
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(set_intersection2(X1,X0))
| ~ empty(set_intersection2(X1,X0))
| one_to_one(set_intersection2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_165])]) ).
fof(f536,plain,
( spl22_55
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_55])]) ).
fof(f586,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(set_intersection2(X1,X0))
| ~ empty(set_intersection2(X1,X0))
| one_to_one(set_intersection2(X1,X0)) )
| ~ spl22_55
| ~ spl22_59 ),
inference(resolution,[],[f553,f537]) ).
fof(f537,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl22_55 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f1504,plain,
( spl22_164
| ~ spl22_41
| ~ spl22_79 ),
inference(avatar_split_clause,[],[f724,f718,f414,f1502]) ).
fof(f724,plain,
( ! [X8,X7] :
( sK7(X7,X8) = apply(X7,sK8(X7,X8))
| sP0(X7,X8)
| ~ empty(X8) )
| ~ spl22_41
| ~ spl22_79 ),
inference(resolution,[],[f719,f415]) ).
fof(f1500,plain,
( ~ spl22_163
| ~ spl22_4
| spl22_5
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1423,f1395,f239,f234,f1497]) ).
fof(f1423,plain,
( ~ in(sK4,relation_dom(sK5))
| ~ sP0(sK5,relation_rng(relation_dom_restriction(sK5,sK3)))
| spl22_5
| ~ spl22_153 ),
inference(resolution,[],[f1396,f241]) ).
fof(f241,plain,
( ~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
| spl22_5 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f1495,plain,
( spl22_162
| ~ spl22_45
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f675,f668,f448,f1493]) ).
fof(f675,plain,
( ! [X2,X3] :
( in(sK8(X2,X3),relation_dom(X2))
| sP0(X2,X3)
| ~ in(X3,sK7(X2,X3)) )
| ~ spl22_45
| ~ spl22_74 ),
inference(resolution,[],[f669,f449]) ).
fof(f1491,plain,
( spl22_161
| ~ spl22_46
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f674,f668,f452,f1489]) ).
fof(f674,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK7(X0,X1),X1) )
| ~ spl22_46
| ~ spl22_74 ),
inference(resolution,[],[f669,f453]) ).
fof(f1487,plain,
( spl22_160
| ~ spl22_45
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f672,f668,f448,f1485]) ).
fof(f672,plain,
( ! [X2,X3] :
( in(sK7(X2,X3),X3)
| sP0(X2,X3)
| ~ in(relation_dom(X2),sK8(X2,X3)) )
| ~ spl22_45
| ~ spl22_74 ),
inference(resolution,[],[f669,f449]) ).
fof(f1483,plain,
( spl22_159
| ~ spl22_46
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f671,f668,f452,f1481]) ).
fof(f671,plain,
( ! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1)
| element(sK8(X0,X1),relation_dom(X0)) )
| ~ spl22_46
| ~ spl22_74 ),
inference(resolution,[],[f669,f453]) ).
fof(f1479,plain,
( spl22_158
| ~ spl22_44
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f562,f536,f444,f1477]) ).
fof(f562,plain,
( ! [X2,X3] :
( ~ function(relation_dom_restriction(X2,X3))
| ~ empty(relation_dom_restriction(X2,X3))
| one_to_one(relation_dom_restriction(X2,X3))
| ~ relation(X2) )
| ~ spl22_44
| ~ spl22_55 ),
inference(resolution,[],[f537,f445]) ).
fof(f1413,plain,
( spl22_157
| ~ spl22_41
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f715,f692,f414,f1411]) ).
fof(f715,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X12)
| sP2(X10,X11,X12)
| ~ empty(X10) )
| ~ spl22_41
| ~ spl22_78 ),
inference(resolution,[],[f693,f415]) ).
fof(f1409,plain,
( spl22_156
| ~ spl22_41
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f711,f692,f414,f1407]) ).
fof(f711,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X10)
| sP2(X10,X11,X12)
| ~ empty(X12) )
| ~ spl22_41
| ~ spl22_78 ),
inference(resolution,[],[f693,f415]) ).
fof(f1405,plain,
( spl22_155
| ~ spl22_41
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f706,f688,f414,f1403]) ).
fof(f706,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X12)
| sP2(X10,X11,X12)
| ~ empty(X11) )
| ~ spl22_41
| ~ spl22_77 ),
inference(resolution,[],[f689,f415]) ).
fof(f1401,plain,
( spl22_154
| ~ spl22_41
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f702,f688,f414,f1399]) ).
fof(f702,plain,
( ! [X10,X11,X12] :
( in(sK13(X10,X11,X12),X11)
| sP2(X10,X11,X12)
| ~ empty(X12) )
| ~ spl22_41
| ~ spl22_77 ),
inference(resolution,[],[f689,f415]) ).
fof(f1397,plain,
( spl22_153
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f682,f678,f1395]) ).
fof(f682,plain,
( ! [X2,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2) )
| ~ spl22_75 ),
inference(equality_resolution,[],[f679]) ).
fof(f1393,plain,
( spl22_152
| ~ spl22_43
| ~ spl22_59 ),
inference(avatar_split_clause,[],[f587,f552,f440,f1391]) ).
fof(f1391,plain,
( spl22_152
<=> ! [X2,X3] :
( ~ relation(X2)
| ~ relation(X3)
| ~ function(set_intersection2(X3,X2))
| sP1(set_intersection2(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_152])]) ).
fof(f440,plain,
( spl22_43
<=> ! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_43])]) ).
fof(f587,plain,
( ! [X2,X3] :
( ~ relation(X2)
| ~ relation(X3)
| ~ function(set_intersection2(X3,X2))
| sP1(set_intersection2(X3,X2)) )
| ~ spl22_43
| ~ spl22_59 ),
inference(resolution,[],[f553,f441]) ).
fof(f441,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP1(X0) )
| ~ spl22_43 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f1375,plain,
( ~ spl22_42
| spl22_151
| ~ spl22_7
| ~ spl22_94
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f863,f846,f812,f249,f1372,f433]) ).
fof(f863,plain,
( apply(relation_dom_restriction(sK15,sK3),sK4) = apply(sK15,sK4)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_94
| ~ spl22_99 ),
inference(forward_demodulation,[],[f862,f814]) ).
fof(f862,plain,
( ~ function(sK15)
| apply(relation_dom_restriction(empty_set,sK3),sK4) = apply(empty_set,sK4)
| ~ spl22_7
| ~ spl22_94
| ~ spl22_99 ),
inference(forward_demodulation,[],[f853,f814]) ).
fof(f853,plain,
( ~ function(empty_set)
| apply(relation_dom_restriction(empty_set,sK3),sK4) = apply(empty_set,sK4)
| ~ spl22_7
| ~ spl22_99 ),
inference(resolution,[],[f847,f251]) ).
fof(f1368,plain,
( spl22_150
| ~ spl22_41
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f676,f668,f414,f1366]) ).
fof(f676,plain,
( ! [X4,X5] :
( in(sK8(X4,X5),relation_dom(X4))
| sP0(X4,X5)
| ~ empty(X5) )
| ~ spl22_41
| ~ spl22_74 ),
inference(resolution,[],[f669,f415]) ).
fof(f1364,plain,
( spl22_149
| ~ spl22_41
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f673,f668,f414,f1362]) ).
fof(f673,plain,
( ! [X4,X5] :
( in(sK7(X4,X5),X5)
| sP0(X4,X5)
| ~ empty(relation_dom(X4)) )
| ~ spl22_41
| ~ spl22_74 ),
inference(resolution,[],[f669,f415]) ).
fof(f1360,plain,
( spl22_148
| ~ spl22_37
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f561,f536,f397,f1358]) ).
fof(f561,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| ~ empty(relation_dom(X1))
| one_to_one(relation_dom(X1))
| ~ empty(X1) )
| ~ spl22_37
| ~ spl22_55 ),
inference(resolution,[],[f537,f398]) ).
fof(f1356,plain,
( spl22_147
| ~ spl22_35
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f560,f536,f389,f1354]) ).
fof(f560,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_55 ),
inference(resolution,[],[f537,f390]) ).
fof(f1318,plain,
( spl22_146
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f716,f692,f1316]) ).
fof(f716,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X0),X0)
| sP2(X0,X1,X0) )
| ~ spl22_78 ),
inference(factoring,[],[f693]) ).
fof(f1314,plain,
( spl22_145
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f707,f688,f1312]) ).
fof(f707,plain,
( ! [X0,X1] :
( in(sK13(X0,X1,X1),X1)
| sP2(X0,X1,X1) )
| ~ spl22_77 ),
inference(factoring,[],[f689]) ).
fof(f1310,plain,
( spl22_144
| ~ spl22_48
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f581,f540,f482,f1308]) ).
fof(f482,plain,
( spl22_48
<=> ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_48])]) ).
fof(f581,plain,
( ! [X2] :
( empty(powerset(X2))
| in(sK6(X2),powerset(X2))
| empty(X2) )
| ~ spl22_48
| ~ spl22_56 ),
inference(resolution,[],[f541,f483]) ).
fof(f483,plain,
( ! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) )
| ~ spl22_48 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f1306,plain,
( spl22_143
| ~ spl22_53
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f580,f540,f502,f1304]) ).
fof(f502,plain,
( spl22_53
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_53])]) ).
fof(f580,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl22_53
| ~ spl22_56 ),
inference(resolution,[],[f541,f503]) ).
fof(f503,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl22_53 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f1302,plain,
( spl22_142
| ~ spl22_43
| ~ spl22_44 ),
inference(avatar_split_clause,[],[f471,f444,f440,f1300]) ).
fof(f471,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| sP1(relation_dom_restriction(X0,X1)) )
| ~ spl22_43
| ~ spl22_44 ),
inference(resolution,[],[f445,f441]) ).
fof(f1279,plain,
( spl22_141
| ~ spl22_48
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f645,f633,f482,f1277]) ).
fof(f645,plain,
( ! [X3,X4] :
( element(X3,X4)
| ~ in(X3,sK6(X4))
| empty(X4) )
| ~ spl22_48
| ~ spl22_67 ),
inference(resolution,[],[f634,f483]) ).
fof(f1275,plain,
( spl22_140
| ~ spl22_53
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f644,f633,f502,f1273]) ).
fof(f1273,plain,
( spl22_140
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_140])]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl22_53
| ~ spl22_67 ),
inference(resolution,[],[f634,f503]) ).
fof(f1271,plain,
( spl22_139
| ~ spl22_20
| ~ spl22_19
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f860,f846,f309,f314,f1268]) ).
fof(f860,plain,
( ~ function(sK20)
| apply(relation_dom_restriction(sK20,sK3),sK4) = apply(sK20,sK4)
| ~ spl22_19
| ~ spl22_99 ),
inference(resolution,[],[f847,f311]) ).
fof(f1266,plain,
( spl22_138
| ~ spl22_51
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f621,f602,f494,f1264]) ).
fof(f1264,plain,
( spl22_138
<=> ! [X6,X4,X5] :
( set_intersection2(X5,X4) != X6
| sP2(X5,X4,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_138])]) ).
fof(f621,plain,
( ! [X6,X4,X5] :
( set_intersection2(X5,X4) != X6
| sP2(X5,X4,X6) )
| ~ spl22_51
| ~ spl22_63 ),
inference(superposition,[],[f603,f495]) ).
fof(f1215,plain,
( spl22_137
| ~ spl22_30
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f646,f633,f359,f1213]) ).
fof(f359,plain,
( spl22_30
<=> ! [X0] : element(sK10(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_30])]) ).
fof(f646,plain,
( ! [X6,X5] :
( element(X5,X6)
| ~ in(X5,sK10(powerset(X6))) )
| ~ spl22_30
| ~ spl22_67 ),
inference(resolution,[],[f634,f360]) ).
fof(f360,plain,
( ! [X0] : element(sK10(X0),X0)
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f1211,plain,
( spl22_136
| ~ spl22_53
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f626,f610,f502,f1209]) ).
fof(f1209,plain,
( spl22_136
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_136])]) ).
fof(f626,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl22_53
| ~ spl22_65 ),
inference(resolution,[],[f611,f503]) ).
fof(f1207,plain,
( spl22_135
| ~ spl22_36
| ~ spl22_54 ),
inference(avatar_split_clause,[],[f526,f506,f393,f1205]) ).
fof(f526,plain,
( ! [X2,X3] :
( relation_dom(X3) = X2
| ~ empty(X2)
| ~ empty(X3) )
| ~ spl22_36
| ~ spl22_54 ),
inference(resolution,[],[f507,f394]) ).
fof(f1200,plain,
( spl22_134
| ~ spl22_34
| ~ spl22_54 ),
inference(avatar_split_clause,[],[f525,f506,f385,f1198]) ).
fof(f525,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl22_34
| ~ spl22_54 ),
inference(resolution,[],[f507,f386]) ).
fof(f1196,plain,
( spl22_133
| ~ spl22_37
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f456,f440,f397,f1194]) ).
fof(f456,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| sP1(relation_dom(X1))
| ~ empty(X1) )
| ~ spl22_37
| ~ spl22_43 ),
inference(resolution,[],[f441,f398]) ).
fof(f1192,plain,
( spl22_132
| ~ spl22_35
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f455,f440,f389,f1190]) ).
fof(f455,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl22_35
| ~ spl22_43 ),
inference(resolution,[],[f441,f390]) ).
fof(f1175,plain,
( spl22_131
| ~ spl22_30
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f628,f610,f359,f1173]) ).
fof(f628,plain,
( ! [X6,X5] :
( ~ empty(X5)
| ~ in(X6,sK10(powerset(X5))) )
| ~ spl22_30
| ~ spl22_65 ),
inference(resolution,[],[f611,f360]) ).
fof(f1171,plain,
( spl22_130
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f625,f602,f381,f373,f264,f1169]) ).
fof(f1169,plain,
( spl22_130
<=> ! [X0,X1] :
( sP2(sK15,X0,X1)
| sK15 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_130])]) ).
fof(f625,plain,
( ! [X0,X1] :
( sP2(sK15,X0,X1)
| sK15 != X1 )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_63 ),
inference(forward_demodulation,[],[f624,f419]) ).
fof(f624,plain,
( ! [X0,X1] :
( sK15 != X1
| sP2(empty_set,X0,X1) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_63 ),
inference(forward_demodulation,[],[f619,f419]) ).
fof(f619,plain,
( ! [X0,X1] :
( empty_set != X1
| sP2(empty_set,X0,X1) )
| ~ spl22_31
| ~ spl22_63 ),
inference(superposition,[],[f603,f374]) ).
fof(f1167,plain,
( spl22_129
| ~ spl22_40
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f620,f602,f410,f1165]) ).
fof(f1165,plain,
( spl22_129
<=> ! [X2,X3] :
( X2 != X3
| sP2(X2,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_129])]) ).
fof(f620,plain,
( ! [X2,X3] :
( X2 != X3
| sP2(X2,X2,X3) )
| ~ spl22_40
| ~ spl22_63 ),
inference(superposition,[],[f603,f411]) ).
fof(f1163,plain,
( spl22_128
| ~ spl22_18
| ~ spl22_17
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f859,f846,f299,f304,f1160]) ).
fof(f859,plain,
( ~ function(sK19)
| apply(relation_dom_restriction(sK19,sK3),sK4) = apply(sK19,sK4)
| ~ spl22_17
| ~ spl22_99 ),
inference(resolution,[],[f847,f301]) ).
fof(f1158,plain,
( spl22_127
| ~ spl22_10
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f585,f540,f406,f381,f343,f264,f1156]) ).
fof(f343,plain,
( spl22_26
<=> ! [X0] : empty(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_26])]) ).
fof(f585,plain,
( ! [X4] :
( in(sK15,powerset(X4))
| empty(powerset(X4)) )
| ~ spl22_10
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_56 ),
inference(forward_demodulation,[],[f584,f419]) ).
fof(f584,plain,
( ! [X4] :
( in(empty_set,powerset(X4))
| empty(powerset(X4)) )
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_56 ),
inference(forward_demodulation,[],[f583,f418]) ).
fof(f418,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl22_26
| ~ spl22_33 ),
inference(resolution,[],[f382,f344]) ).
fof(f344,plain,
( ! [X0] : empty(sK11(X0))
| ~ spl22_26 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f583,plain,
( ! [X4] :
( empty(powerset(X4))
| in(sK11(X4),powerset(X4)) )
| ~ spl22_39
| ~ spl22_56 ),
inference(resolution,[],[f541,f407]) ).
fof(f1113,plain,
( spl22_126
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f623,f602,f1111]) ).
fof(f623,plain,
( ! [X0,X1] : sP2(X0,X1,set_intersection2(X1,X0))
| ~ spl22_63 ),
inference(equality_resolution,[],[f603]) ).
fof(f1109,plain,
( spl22_125
| ~ spl22_61 ),
inference(avatar_split_clause,[],[f618,f594,f1107]) ).
fof(f618,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) )
| ~ spl22_61 ),
inference(equality_resolution,[],[f595]) ).
fof(f1105,plain,
( spl22_124
| ~ spl22_30
| ~ spl22_56 ),
inference(avatar_split_clause,[],[f582,f540,f359,f1103]) ).
fof(f582,plain,
( ! [X3] :
( empty(X3)
| in(sK10(X3),X3) )
| ~ spl22_30
| ~ spl22_56 ),
inference(resolution,[],[f541,f360]) ).
fof(f1098,plain,
( ~ spl22_42
| ~ spl22_10
| spl22_123
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f573,f536,f381,f264,f249,f1095,f264,f433]) ).
fof(f1095,plain,
( spl22_123
<=> one_to_one(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_123])]) ).
fof(f573,plain,
( one_to_one(sK15)
| ~ empty(sK15)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_55 ),
inference(forward_demodulation,[],[f572,f419]) ).
fof(f572,plain,
( ~ empty(sK15)
| ~ function(sK15)
| one_to_one(empty_set)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_55 ),
inference(forward_demodulation,[],[f571,f419]) ).
fof(f571,plain,
( ~ function(sK15)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_55 ),
inference(forward_demodulation,[],[f563,f419]) ).
fof(f563,plain,
( ~ function(empty_set)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl22_7
| ~ spl22_55 ),
inference(resolution,[],[f537,f251]) ).
fof(f1093,plain,
( spl22_121
| ~ spl22_122
| ~ spl22_18
| ~ spl22_17
| ~ spl22_55 ),
inference(avatar_split_clause,[],[f568,f536,f299,f304,f1090,f1086]) ).
fof(f1086,plain,
( spl22_121
<=> one_to_one(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_121])]) ).
fof(f568,plain,
( ~ function(sK19)
| ~ empty(sK19)
| one_to_one(sK19)
| ~ spl22_17
| ~ spl22_55 ),
inference(resolution,[],[f537,f301]) ).
fof(f1084,plain,
( spl22_120
| ~ spl22_48
| ~ spl22_52 ),
inference(avatar_split_clause,[],[f521,f498,f482,f1082]) ).
fof(f1082,plain,
( spl22_120
<=> ! [X2] :
( subset(sK6(X2),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_120])]) ).
fof(f521,plain,
( ! [X2] :
( subset(sK6(X2),X2)
| empty(X2) )
| ~ spl22_48
| ~ spl22_52 ),
inference(resolution,[],[f499,f483]) ).
fof(f1080,plain,
( spl22_119
| ~ spl22_10
| ~ spl22_33
| ~ spl22_36 ),
inference(avatar_split_clause,[],[f431,f393,f381,f264,f1078]) ).
fof(f431,plain,
( ! [X0] :
( relation_dom(X0) = sK15
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_33
| ~ spl22_36 ),
inference(forward_demodulation,[],[f428,f419]) ).
fof(f428,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set )
| ~ spl22_33
| ~ spl22_36 ),
inference(resolution,[],[f394,f382]) ).
fof(f1076,plain,
( spl22_118
| ~ spl22_10
| ~ spl22_33
| ~ spl22_34 ),
inference(avatar_split_clause,[],[f427,f385,f381,f264,f1074]) ).
fof(f427,plain,
( ! [X0] :
( relation_rng(X0) = sK15
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_33
| ~ spl22_34 ),
inference(forward_demodulation,[],[f424,f419]) ).
fof(f424,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set )
| ~ spl22_33
| ~ spl22_34 ),
inference(resolution,[],[f386,f382]) ).
fof(f1065,plain,
( spl22_117
| ~ spl22_2
| ~ spl22_1
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f854,f846,f219,f224,f1062]) ).
fof(f854,plain,
( ~ function(sK5)
| apply(sK5,sK4) = apply(relation_dom_restriction(sK5,sK3),sK4)
| ~ spl22_1
| ~ spl22_99 ),
inference(resolution,[],[f847,f221]) ).
fof(f1005,plain,
( spl22_114
| ~ spl22_33
| ~ spl22_94 ),
inference(avatar_split_clause,[],[f972,f812,f381,f952]) ).
fof(f972,plain,
( ! [X0] :
( sK15 = X0
| ~ empty(X0) )
| ~ spl22_33
| ~ spl22_94 ),
inference(forward_demodulation,[],[f382,f814]) ).
fof(f971,plain,
( ~ spl22_6
| ~ spl22_115 ),
inference(avatar_contradiction_clause,[],[f962]) ).
fof(f962,plain,
( $false
| ~ spl22_6
| ~ spl22_115 ),
inference(resolution,[],[f957,f246]) ).
fof(f957,plain,
( ! [X7] : ~ empty(X7)
| ~ spl22_115 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f970,plain,
( ~ spl22_26
| ~ spl22_115 ),
inference(avatar_contradiction_clause,[],[f963]) ).
fof(f963,plain,
( $false
| ~ spl22_26
| ~ spl22_115 ),
inference(resolution,[],[f957,f344]) ).
fof(f969,plain,
( ~ spl22_10
| ~ spl22_115 ),
inference(avatar_contradiction_clause,[],[f964]) ).
fof(f964,plain,
( $false
| ~ spl22_10
| ~ spl22_115 ),
inference(resolution,[],[f957,f266]) ).
fof(f968,plain,
( ~ spl22_13
| ~ spl22_115 ),
inference(avatar_contradiction_clause,[],[f965]) ).
fof(f965,plain,
( $false
| ~ spl22_13
| ~ spl22_115 ),
inference(resolution,[],[f957,f281]) ).
fof(f281,plain,
( empty(sK17)
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f279,plain,
( spl22_13
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_13])]) ).
fof(f967,plain,
( ~ spl22_23
| ~ spl22_115 ),
inference(avatar_contradiction_clause,[],[f966]) ).
fof(f966,plain,
( $false
| ~ spl22_23
| ~ spl22_115 ),
inference(resolution,[],[f957,f331]) ).
fof(f331,plain,
( empty(sK21)
| ~ spl22_23 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f329,plain,
( spl22_23
<=> empty(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_23])]) ).
fof(f961,plain,
( spl22_115
| spl22_116
| ~ spl22_10
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f631,f610,f406,f381,f343,f264,f959,f956]) ).
fof(f631,plain,
( ! [X8,X7] :
( ~ in(X8,sK15)
| ~ empty(X7) )
| ~ spl22_10
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_65 ),
inference(forward_demodulation,[],[f630,f419]) ).
fof(f630,plain,
( ! [X8,X7] :
( ~ in(X8,empty_set)
| ~ empty(X7) )
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_65 ),
inference(forward_demodulation,[],[f629,f418]) ).
fof(f629,plain,
( ! [X8,X7] :
( ~ empty(X7)
| ~ in(X8,sK11(X7)) )
| ~ spl22_39
| ~ spl22_65 ),
inference(resolution,[],[f611,f407]) ).
fof(f954,plain,
( spl22_114
| ~ spl22_10
| ~ spl22_54 ),
inference(avatar_split_clause,[],[f529,f506,f264,f952]) ).
fof(f529,plain,
( ! [X7] :
( sK15 = X7
| ~ empty(X7) )
| ~ spl22_10
| ~ spl22_54 ),
inference(resolution,[],[f507,f266]) ).
fof(f950,plain,
( spl22_113
| ~ spl22_30
| ~ spl22_52 ),
inference(avatar_split_clause,[],[f519,f498,f359,f948]) ).
fof(f948,plain,
( spl22_113
<=> ! [X0] : subset(sK10(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_113])]) ).
fof(f519,plain,
( ! [X0] : subset(sK10(powerset(X0)),X0)
| ~ spl22_30
| ~ spl22_52 ),
inference(resolution,[],[f499,f360]) ).
fof(f946,plain,
( spl22_112
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_51 ),
inference(avatar_split_clause,[],[f515,f494,f381,f373,f264,f944]) ).
fof(f515,plain,
( ! [X0] : sK15 = set_intersection2(sK15,X0)
| ~ spl22_10
| ~ spl22_31
| ~ spl22_33
| ~ spl22_51 ),
inference(forward_demodulation,[],[f511,f419]) ).
fof(f511,plain,
( ! [X0] : empty_set = set_intersection2(empty_set,X0)
| ~ spl22_31
| ~ spl22_51 ),
inference(superposition,[],[f495,f374]) ).
fof(f942,plain,
( spl22_111
| ~ spl22_28
| ~ spl22_36 ),
inference(avatar_split_clause,[],[f430,f393,f351,f940]) ).
fof(f430,plain,
( ! [X2] :
( ~ empty(X2)
| function(relation_dom(X2)) )
| ~ spl22_28
| ~ spl22_36 ),
inference(resolution,[],[f394,f352]) ).
fof(f938,plain,
( spl22_110
| ~ spl22_28
| ~ spl22_34 ),
inference(avatar_split_clause,[],[f426,f385,f351,f936]) ).
fof(f426,plain,
( ! [X2] :
( ~ empty(X2)
| function(relation_rng(X2)) )
| ~ spl22_28
| ~ spl22_34 ),
inference(resolution,[],[f386,f352]) ).
fof(f932,plain,
( spl22_109
| ~ spl22_94
| ~ spl22_101 ),
inference(avatar_split_clause,[],[f895,f892,f812,f930]) ).
fof(f892,plain,
( spl22_101
<=> ! [X0] : empty_set = sK11(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_101])]) ).
fof(f895,plain,
( ! [X0] : sK11(X0) = sK15
| ~ spl22_94
| ~ spl22_101 ),
inference(forward_demodulation,[],[f893,f814]) ).
fof(f893,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl22_101 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f928,plain,
( ~ spl22_42
| spl22_108
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f466,f440,f381,f264,f249,f925,f433]) ).
fof(f466,plain,
( sP1(sK15)
| ~ function(sK15)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_43 ),
inference(forward_demodulation,[],[f465,f419]) ).
fof(f465,plain,
( ~ function(sK15)
| sP1(empty_set)
| ~ spl22_7
| ~ spl22_10
| ~ spl22_33
| ~ spl22_43 ),
inference(forward_demodulation,[],[f457,f419]) ).
fof(f457,plain,
( ~ function(empty_set)
| sP1(empty_set)
| ~ spl22_7
| ~ spl22_43 ),
inference(resolution,[],[f441,f251]) ).
fof(f923,plain,
( spl22_107
| ~ spl22_20
| ~ spl22_19
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f463,f440,f309,f314,f920]) ).
fof(f463,plain,
( ~ function(sK20)
| sP1(sK20)
| ~ spl22_19
| ~ spl22_43 ),
inference(resolution,[],[f441,f311]) ).
fof(f918,plain,
( spl22_106
| ~ spl22_18
| ~ spl22_17
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f462,f440,f299,f304,f915]) ).
fof(f462,plain,
( ~ function(sK19)
| sP1(sK19)
| ~ spl22_17
| ~ spl22_43 ),
inference(resolution,[],[f441,f301]) ).
fof(f913,plain,
( spl22_104
| ~ spl22_105
| ~ spl22_15
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f461,f440,f289,f910,f906]) ).
fof(f906,plain,
( spl22_104
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_104])]) ).
fof(f910,plain,
( spl22_105
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_105])]) ).
fof(f289,plain,
( spl22_15
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_15])]) ).
fof(f461,plain,
( ~ function(sK18)
| sP1(sK18)
| ~ spl22_15
| ~ spl22_43 ),
inference(resolution,[],[f441,f291]) ).
fof(f291,plain,
( relation(sK18)
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f904,plain,
( spl22_102
| ~ spl22_103
| ~ spl22_12
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f459,f440,f274,f901,f897]) ).
fof(f897,plain,
( spl22_102
<=> sP1(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_102])]) ).
fof(f901,plain,
( spl22_103
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_103])]) ).
fof(f274,plain,
( spl22_12
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).
fof(f459,plain,
( ~ function(sK16)
| sP1(sK16)
| ~ spl22_12
| ~ spl22_43 ),
inference(resolution,[],[f441,f276]) ).
fof(f276,plain,
( relation(sK16)
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f894,plain,
( spl22_101
| ~ spl22_26
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f418,f381,f343,f892]) ).
fof(f871,plain,
( spl22_100
| ~ spl22_4
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f696,f684,f234,f869]) ).
fof(f696,plain,
( ! [X1] :
( apply(relation_dom_restriction(X1,relation_dom(sK5)),sK4) = apply(X1,sK4)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl22_4
| ~ spl22_76 ),
inference(resolution,[],[f685,f236]) ).
fof(f848,plain,
( spl22_99
| ~ spl22_3
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f695,f684,f229,f846]) ).
fof(f695,plain,
( ! [X0] :
( apply(relation_dom_restriction(X0,sK3),sK4) = apply(X0,sK4)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl22_3
| ~ spl22_76 ),
inference(resolution,[],[f685,f231]) ).
fof(f231,plain,
( in(sK4,sK3)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f839,plain,
( spl22_98
| ~ spl22_8
| ~ spl22_94 ),
inference(avatar_split_clause,[],[f832,f812,f254,f836]) ).
fof(f836,plain,
( spl22_98
<=> relation_empty_yielding(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_98])]) ).
fof(f254,plain,
( spl22_8
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).
fof(f832,plain,
( relation_empty_yielding(sK15)
| ~ spl22_8
| ~ spl22_94 ),
inference(superposition,[],[f256,f814]) ).
fof(f256,plain,
( relation_empty_yielding(empty_set)
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f829,plain,
( spl22_97
| ~ spl22_10
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_52 ),
inference(avatar_split_clause,[],[f523,f498,f406,f381,f343,f264,f827]) ).
fof(f827,plain,
( spl22_97
<=> ! [X1] : subset(sK15,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_97])]) ).
fof(f523,plain,
( ! [X1] : subset(sK15,X1)
| ~ spl22_10
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_52 ),
inference(forward_demodulation,[],[f522,f419]) ).
fof(f522,plain,
( ! [X1] : subset(empty_set,X1)
| ~ spl22_26
| ~ spl22_33
| ~ spl22_39
| ~ spl22_52 ),
inference(forward_demodulation,[],[f520,f418]) ).
fof(f520,plain,
( ! [X1] : subset(sK11(X1),X1)
| ~ spl22_39
| ~ spl22_52 ),
inference(resolution,[],[f499,f407]) ).
fof(f825,plain,
( spl22_96
| ~ spl22_10
| ~ spl22_23
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f423,f381,f329,f264,f822]) ).
fof(f822,plain,
( spl22_96
<=> sK15 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_96])]) ).
fof(f423,plain,
( sK15 = sK21
| ~ spl22_10
| ~ spl22_23
| ~ spl22_33 ),
inference(forward_demodulation,[],[f421,f419]) ).
fof(f421,plain,
( empty_set = sK21
| ~ spl22_23
| ~ spl22_33 ),
inference(resolution,[],[f382,f331]) ).
fof(f820,plain,
( spl22_95
| ~ spl22_10
| ~ spl22_13
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f422,f381,f279,f264,f817]) ).
fof(f817,plain,
( spl22_95
<=> sK15 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_95])]) ).
fof(f422,plain,
( sK15 = sK17
| ~ spl22_10
| ~ spl22_13
| ~ spl22_33 ),
inference(forward_demodulation,[],[f420,f419]) ).
fof(f420,plain,
( empty_set = sK17
| ~ spl22_13
| ~ spl22_33 ),
inference(resolution,[],[f382,f281]) ).
fof(f815,plain,
( spl22_94
| ~ spl22_10
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f419,f381,f264,f812]) ).
fof(f809,plain,
( spl22_93
| ~ spl22_26
| ~ spl22_29 ),
inference(avatar_split_clause,[],[f368,f355,f343,f807]) ).
fof(f807,plain,
( spl22_93
<=> ! [X0] : relation(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_93])]) ).
fof(f368,plain,
( ! [X0] : relation(sK11(X0))
| ~ spl22_26
| ~ spl22_29 ),
inference(resolution,[],[f356,f344]) ).
fof(f804,plain,
( spl22_92
| ~ spl22_26
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f363,f351,f343,f802]) ).
fof(f802,plain,
( spl22_92
<=> ! [X0] : function(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_92])]) ).
fof(f363,plain,
( ! [X0] : function(sK11(X0))
| ~ spl22_26
| ~ spl22_28 ),
inference(resolution,[],[f352,f344]) ).
fof(f798,plain,
( spl22_91
| ~ spl22_10
| ~ spl22_29 ),
inference(avatar_split_clause,[],[f369,f355,f264,f795]) ).
fof(f369,plain,
( relation(sK15)
| ~ spl22_10
| ~ spl22_29 ),
inference(resolution,[],[f356,f266]) ).
fof(f792,plain,
( spl22_90
| ~ spl22_13
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f365,f351,f279,f789]) ).
fof(f789,plain,
( spl22_90
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_90])]) ).
fof(f365,plain,
( function(sK17)
| ~ spl22_13
| ~ spl22_28 ),
inference(resolution,[],[f352,f281]) ).
fof(f786,plain,
( spl22_89
| ~ spl22_4
| ~ spl22_46 ),
inference(avatar_split_clause,[],[f480,f452,f234,f783]) ).
fof(f783,plain,
( spl22_89
<=> element(sK4,relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_89])]) ).
fof(f480,plain,
( element(sK4,relation_dom(sK5))
| ~ spl22_4
| ~ spl22_46 ),
inference(resolution,[],[f453,f236]) ).
fof(f781,plain,
( ~ spl22_88
| ~ spl22_4
| ~ spl22_45 ),
inference(avatar_split_clause,[],[f473,f448,f234,f778]) ).
fof(f778,plain,
( spl22_88
<=> in(relation_dom(sK5),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_88])]) ).
fof(f473,plain,
( ~ in(relation_dom(sK5),sK4)
| ~ spl22_4
| ~ spl22_45 ),
inference(resolution,[],[f449,f236]) ).
fof(f776,plain,
( spl22_87
| ~ spl22_2
| ~ spl22_1
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f458,f440,f219,f224,f773]) ).
fof(f458,plain,
( ~ function(sK5)
| sP1(sK5)
| ~ spl22_1
| ~ spl22_43 ),
inference(resolution,[],[f441,f221]) ).
fof(f768,plain,
spl22_86,
inference(avatar_split_clause,[],[f185,f766]) ).
fof(f185,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
& in(sK12(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f106,f107]) ).
fof(f107,plain,
! [X1,X2] :
( ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2))
& in(sK12(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t68_funct_1) ).
fof(f757,plain,
spl22_85,
inference(avatar_split_clause,[],[f184,f755]) ).
fof(f184,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK12(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f752,plain,
spl22_84,
inference(avatar_split_clause,[],[f183,f750]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f742,plain,
spl22_83,
inference(avatar_split_clause,[],[f198,f740]) ).
fof(f198,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f112,f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f111]) ).
fof(f111,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f737,plain,
spl22_82,
inference(avatar_split_clause,[],[f182,f735]) ).
fof(f182,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f733,plain,
( ~ spl22_81
| ~ spl22_36
| spl22_60 ),
inference(avatar_split_clause,[],[f681,f556,f393,f730]) ).
fof(f556,plain,
( spl22_60
<=> empty(relation_dom(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_60])]) ).
fof(f681,plain,
( ~ empty(sK5)
| ~ spl22_36
| spl22_60 ),
inference(resolution,[],[f558,f394]) ).
fof(f558,plain,
( ~ empty(relation_dom(sK5))
| spl22_60 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f728,plain,
spl22_80,
inference(avatar_split_clause,[],[f163,f726]) ).
fof(f163,plain,
! [X3,X0,X1] :
( sP0(X0,X1)
| apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK7(X0,X1),X1) )
& ( ( sK7(X0,X1) = apply(X0,sK8(X0,X1))
& in(sK8(X0,X1),relation_dom(X0)) )
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK9(X0,X5)) = X5
& in(sK9(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f95,f98,f97,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK7(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK7(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK7(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK7(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK7(X0,X1) = apply(X0,sK8(X0,X1))
& in(sK8(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK9(X0,X5)) = X5
& in(sK9(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f720,plain,
spl22_79,
inference(avatar_split_clause,[],[f162,f718]) ).
fof(f162,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK7(X0,X1) = apply(X0,sK8(X0,X1))
| in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f694,plain,
spl22_78,
inference(avatar_split_clause,[],[f197,f692]) ).
fof(f197,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X0)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f690,plain,
spl22_77,
inference(avatar_split_clause,[],[f196,f688]) ).
fof(f196,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f686,plain,
spl22_76,
inference(avatar_split_clause,[],[f191,f684]) ).
fof(f191,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t72_funct_1) ).
fof(f680,plain,
spl22_75,
inference(avatar_split_clause,[],[f160,f678]) ).
fof(f160,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f670,plain,
spl22_74,
inference(avatar_split_clause,[],[f161,f668]) ).
fof(f161,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(sK8(X0,X1),relation_dom(X0))
| in(sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f666,plain,
spl22_73,
inference(avatar_split_clause,[],[f195,f664]) ).
fof(f195,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f662,plain,
spl22_72,
inference(avatar_split_clause,[],[f159,f660]) ).
fof(f159,plain,
! [X0,X1,X5] :
( apply(X0,sK9(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f658,plain,
spl22_71,
inference(avatar_split_clause,[],[f158,f656]) ).
fof(f158,plain,
! [X0,X1,X5] :
( in(sK9(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f654,plain,
( spl22_70
| ~ spl22_3
| ~ spl22_46 ),
inference(avatar_split_clause,[],[f479,f452,f229,f651]) ).
fof(f651,plain,
( spl22_70
<=> element(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_70])]) ).
fof(f479,plain,
( element(sK4,sK3)
| ~ spl22_3
| ~ spl22_46 ),
inference(resolution,[],[f453,f231]) ).
fof(f643,plain,
spl22_69,
inference(avatar_split_clause,[],[f194,f641]) ).
fof(f194,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f639,plain,
spl22_68,
inference(avatar_split_clause,[],[f193,f637]) ).
fof(f193,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f635,plain,
spl22_67,
inference(avatar_split_clause,[],[f192,f633]) ).
fof(f192,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t4_subset) ).
fof(f617,plain,
( ~ spl22_66
| ~ spl22_3
| ~ spl22_45 ),
inference(avatar_split_clause,[],[f472,f448,f229,f614]) ).
fof(f614,plain,
( spl22_66
<=> in(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_66])]) ).
fof(f472,plain,
( ~ in(sK3,sK4)
| ~ spl22_3
| ~ spl22_45 ),
inference(resolution,[],[f449,f231]) ).
fof(f612,plain,
spl22_65,
inference(avatar_split_clause,[],[f201,f610]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t5_subset) ).
fof(f608,plain,
spl22_64,
inference(avatar_split_clause,[],[f200,f606]) ).
fof(f200,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP2(X1,X0,X2) ),
inference(definition_folding,[],[f6,f87]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',d3_xboole_0) ).
fof(f604,plain,
spl22_63,
inference(avatar_split_clause,[],[f199,f602]) ).
fof(f199,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f115]) ).
fof(f600,plain,
spl22_62,
inference(avatar_split_clause,[],[f157,f598]) ).
fof(f157,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f596,plain,
spl22_61,
inference(avatar_split_clause,[],[f156,f594]) ).
fof(f156,plain,
! [X0,X1] :
( sP0(X0,X1)
| relation_rng(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f559,plain,
( ~ spl22_60
| ~ spl22_4
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f438,f414,f234,f556]) ).
fof(f438,plain,
( ~ empty(relation_dom(sK5))
| ~ spl22_4
| ~ spl22_41 ),
inference(resolution,[],[f415,f236]) ).
fof(f554,plain,
spl22_59,
inference(avatar_split_clause,[],[f186,f552]) ).
fof(f186,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc1_relat_1) ).
fof(f550,plain,
spl22_58,
inference(avatar_split_clause,[],[f181,f548]) ).
fof(f181,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc4_funct_1) ).
fof(f546,plain,
spl22_57,
inference(avatar_split_clause,[],[f179,f544]) ).
fof(f544,plain,
( spl22_57
<=> ! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_57])]) ).
fof(f179,plain,
! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc13_relat_1) ).
fof(f542,plain,
spl22_56,
inference(avatar_split_clause,[],[f177,f540]) ).
fof(f177,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t2_subset) ).
fof(f538,plain,
spl22_55,
inference(avatar_split_clause,[],[f167,f536]) ).
fof(f167,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',cc2_funct_1) ).
fof(f508,plain,
spl22_54,
inference(avatar_split_clause,[],[f189,f506]) ).
fof(f189,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t8_boole) ).
fof(f504,plain,
spl22_53,
inference(avatar_split_clause,[],[f188,f502]) ).
fof(f188,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t3_subset) ).
fof(f500,plain,
spl22_52,
inference(avatar_split_clause,[],[f187,f498]) ).
fof(f187,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f496,plain,
spl22_51,
inference(avatar_split_clause,[],[f173,f494]) ).
fof(f173,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',commutativity_k3_xboole_0) ).
fof(f492,plain,
spl22_50,
inference(avatar_split_clause,[],[f155,f490]) ).
fof(f490,plain,
( spl22_50
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_50])]) ).
fof(f155,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc5_relat_1) ).
fof(f488,plain,
spl22_49,
inference(avatar_split_clause,[],[f154,f486]) ).
fof(f154,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc6_relat_1) ).
fof(f484,plain,
spl22_48,
inference(avatar_split_clause,[],[f145,f482]) ).
fof(f145,plain,
! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f50,f91]) ).
fof(f91,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc1_subset_1) ).
fof(f478,plain,
( ~ spl22_47
| ~ spl22_3
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f437,f414,f229,f475]) ).
fof(f437,plain,
( ~ empty(sK3)
| ~ spl22_3
| ~ spl22_41 ),
inference(resolution,[],[f415,f231]) ).
fof(f454,plain,
spl22_46,
inference(avatar_split_clause,[],[f176,f452]) ).
fof(f176,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t1_subset) ).
fof(f450,plain,
spl22_45,
inference(avatar_split_clause,[],[f175,f448]) ).
fof(f175,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',antisymmetry_r2_hidden) ).
fof(f446,plain,
spl22_44,
inference(avatar_split_clause,[],[f174,f444]) ).
fof(f174,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',dt_k7_relat_1) ).
fof(f442,plain,
spl22_43,
inference(avatar_split_clause,[],[f164,f440]) ).
fof(f164,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f61,f85,f84]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',d5_funct_1) ).
fof(f436,plain,
( spl22_42
| ~ spl22_10
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f364,f351,f264,f433]) ).
fof(f364,plain,
( function(sK15)
| ~ spl22_10
| ~ spl22_28 ),
inference(resolution,[],[f352,f266]) ).
fof(f416,plain,
spl22_41,
inference(avatar_split_clause,[],[f190,f414]) ).
fof(f190,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t7_boole) ).
fof(f412,plain,
spl22_40,
inference(avatar_split_clause,[],[f172,f410]) ).
fof(f172,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',idempotence_k3_xboole_0) ).
fof(f408,plain,
spl22_39,
inference(avatar_split_clause,[],[f169,f406]) ).
fof(f169,plain,
! [X0] : element(sK11(X0),powerset(X0)),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f28,f102]) ).
fof(f102,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc2_subset_1) ).
fof(f404,plain,
( spl22_38
| ~ spl22_6
| ~ spl22_28 ),
inference(avatar_split_clause,[],[f362,f351,f244,f401]) ).
fof(f401,plain,
( spl22_38
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_38])]) ).
fof(f362,plain,
( function(empty_set)
| ~ spl22_6
| ~ spl22_28 ),
inference(resolution,[],[f352,f246]) ).
fof(f399,plain,
spl22_37,
inference(avatar_split_clause,[],[f153,f397]) ).
fof(f153,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc7_relat_1) ).
fof(f395,plain,
spl22_36,
inference(avatar_split_clause,[],[f152,f393]) ).
fof(f152,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f391,plain,
spl22_35,
inference(avatar_split_clause,[],[f151,f389]) ).
fof(f151,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc8_relat_1) ).
fof(f387,plain,
spl22_34,
inference(avatar_split_clause,[],[f150,f385]) ).
fof(f150,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f383,plain,
spl22_33,
inference(avatar_split_clause,[],[f149,f381]) ).
fof(f149,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t6_boole) ).
fof(f379,plain,
spl22_32,
inference(avatar_split_clause,[],[f146,f377]) ).
fof(f377,plain,
( spl22_32
<=> ! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_32])]) ).
fof(f146,plain,
! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f375,plain,
spl22_31,
inference(avatar_split_clause,[],[f144,f373]) ).
fof(f144,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t2_boole) ).
fof(f361,plain,
spl22_30,
inference(avatar_split_clause,[],[f168,f359]) ).
fof(f168,plain,
! [X0] : element(sK10(X0),X0),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] : element(sK10(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f9,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',existence_m1_subset_1) ).
fof(f357,plain,
spl22_29,
inference(avatar_split_clause,[],[f148,f355]) ).
fof(f148,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',cc1_relat_1) ).
fof(f353,plain,
spl22_28,
inference(avatar_split_clause,[],[f147,f351]) ).
fof(f147,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',cc1_funct_1) ).
fof(f349,plain,
spl22_27,
inference(avatar_split_clause,[],[f171,f347]) ).
fof(f171,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',reflexivity_r1_tarski) ).
fof(f345,plain,
spl22_26,
inference(avatar_split_clause,[],[f170,f343]) ).
fof(f170,plain,
! [X0] : empty(sK11(X0)),
inference(cnf_transformation,[],[f103]) ).
fof(f341,plain,
spl22_25,
inference(avatar_split_clause,[],[f143,f339]) ).
fof(f143,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc1_subset_1) ).
fof(f337,plain,
spl22_24,
inference(avatar_split_clause,[],[f217,f334]) ).
fof(f334,plain,
( spl22_24
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_24])]) ).
fof(f217,plain,
function(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( function(sK21)
& empty(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f26,f130]) ).
fof(f130,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK21)
& empty(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc2_funct_1) ).
fof(f332,plain,
spl22_23,
inference(avatar_split_clause,[],[f216,f329]) ).
fof(f216,plain,
empty(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f327,plain,
spl22_22,
inference(avatar_split_clause,[],[f215,f324]) ).
fof(f324,plain,
( spl22_22
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_22])]) ).
fof(f215,plain,
relation(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f322,plain,
spl22_21,
inference(avatar_split_clause,[],[f214,f319]) ).
fof(f319,plain,
( spl22_21
<=> one_to_one(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_21])]) ).
fof(f214,plain,
one_to_one(sK20),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( one_to_one(sK20)
& function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f30,f128]) ).
fof(f128,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK20)
& function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc3_funct_1) ).
fof(f317,plain,
spl22_20,
inference(avatar_split_clause,[],[f213,f314]) ).
fof(f213,plain,
function(sK20),
inference(cnf_transformation,[],[f129]) ).
fof(f312,plain,
spl22_19,
inference(avatar_split_clause,[],[f212,f309]) ).
fof(f212,plain,
relation(sK20),
inference(cnf_transformation,[],[f129]) ).
fof(f307,plain,
spl22_18,
inference(avatar_split_clause,[],[f211,f304]) ).
fof(f211,plain,
function(sK19),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f22,f126]) ).
fof(f126,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc1_funct_1) ).
fof(f302,plain,
spl22_17,
inference(avatar_split_clause,[],[f210,f299]) ).
fof(f210,plain,
relation(sK19),
inference(cnf_transformation,[],[f127]) ).
fof(f297,plain,
spl22_16,
inference(avatar_split_clause,[],[f209,f294]) ).
fof(f294,plain,
( spl22_16
<=> relation_empty_yielding(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_16])]) ).
fof(f209,plain,
relation_empty_yielding(sK18),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
( relation_empty_yielding(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f31,f124]) ).
fof(f124,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc3_relat_1) ).
fof(f292,plain,
spl22_15,
inference(avatar_split_clause,[],[f208,f289]) ).
fof(f208,plain,
relation(sK18),
inference(cnf_transformation,[],[f125]) ).
fof(f287,plain,
spl22_14,
inference(avatar_split_clause,[],[f207,f284]) ).
fof(f284,plain,
( spl22_14
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_14])]) ).
fof(f207,plain,
relation(sK17),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( relation(sK17)
& empty(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f23,f122]) ).
fof(f122,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK17)
& empty(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc1_relat_1) ).
fof(f282,plain,
spl22_13,
inference(avatar_split_clause,[],[f206,f279]) ).
fof(f206,plain,
empty(sK17),
inference(cnf_transformation,[],[f123]) ).
fof(f277,plain,
spl22_12,
inference(avatar_split_clause,[],[f205,f274]) ).
fof(f205,plain,
relation(sK16),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f27,f120]) ).
fof(f120,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK16)
& ~ empty(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc2_relat_1) ).
fof(f272,plain,
~ spl22_11,
inference(avatar_split_clause,[],[f204,f269]) ).
fof(f204,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f121]) ).
fof(f267,plain,
spl22_10,
inference(avatar_split_clause,[],[f203,f264]) ).
fof(f203,plain,
empty(sK15),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
empty(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f25,f118]) ).
fof(f118,plain,
( ? [X0] : empty(X0)
=> empty(sK15) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc1_xboole_0) ).
fof(f262,plain,
~ spl22_9,
inference(avatar_split_clause,[],[f202,f259]) ).
fof(f202,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
~ empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f29,f116]) ).
fof(f116,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',rc2_xboole_0) ).
fof(f257,plain,
spl22_8,
inference(avatar_split_clause,[],[f142,f254]) ).
fof(f142,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc12_relat_1) ).
fof(f252,plain,
spl22_7,
inference(avatar_split_clause,[],[f139,f249]) ).
fof(f139,plain,
relation(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc4_relat_1) ).
fof(f247,plain,
spl22_6,
inference(avatar_split_clause,[],[f137,f244]) ).
fof(f137,plain,
empty(empty_set),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',fc1_xboole_0) ).
fof(f242,plain,
~ spl22_5,
inference(avatar_split_clause,[],[f136,f239]) ).
fof(f136,plain,
~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3))),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
& in(sK4,sK3)
& in(sK4,relation_dom(sK5))
& function(sK5)
& relation(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f49,f89]) ).
fof(f89,plain,
( ? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) )
=> ( ~ in(apply(sK5,sK4),relation_rng(relation_dom_restriction(sK5,sK3)))
& in(sK4,sK3)
& in(sK4,relation_dom(sK5))
& function(sK5)
& relation(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,X0)
& in(X1,relation_dom(X2))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
inference(negated_conjecture,[],[f42]) ).
fof(f42,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( in(X1,X0)
& in(X1,relation_dom(X2)) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6rUbysz7bu/Vampire---4.8_6630',t73_funct_1) ).
fof(f237,plain,
spl22_4,
inference(avatar_split_clause,[],[f134,f234]) ).
fof(f134,plain,
in(sK4,relation_dom(sK5)),
inference(cnf_transformation,[],[f90]) ).
fof(f232,plain,
spl22_3,
inference(avatar_split_clause,[],[f135,f229]) ).
fof(f135,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f90]) ).
fof(f227,plain,
spl22_2,
inference(avatar_split_clause,[],[f133,f224]) ).
fof(f133,plain,
function(sK5),
inference(cnf_transformation,[],[f90]) ).
fof(f222,plain,
spl22_1,
inference(avatar_split_clause,[],[f132,f219]) ).
fof(f132,plain,
relation(sK5),
inference(cnf_transformation,[],[f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SEU039+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.10 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.09/0.29 % Computer : n006.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 30 14:12:05 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.32 % (7675)Running in auto input_syntax mode. Trying TPTP
% 0.09/0.32 % (7772)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.09/0.32 % (7771)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.09/0.32 % (7773)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.09/0.32 % (7774)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.09/0.32 % (7769)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.09/0.32 % (7777)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.09/0.32 % (7776)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.09/0.32 TRYING [1]
% 0.09/0.32 TRYING [2]
% 0.09/0.33 TRYING [3]
% 0.09/0.33 TRYING [1]
% 0.09/0.33 TRYING [2]
% 0.09/0.34 TRYING [4]
% 0.09/0.36 TRYING [3]
% 0.14/0.37 TRYING [5]
% 0.14/0.41 TRYING [4]
% 0.14/0.43 TRYING [6]
% 0.14/0.54 TRYING [5]
% 0.14/0.55 TRYING [7]
% 3.93/0.91 TRYING [8]
% 5.04/1.03 TRYING [6]
% 7.64/1.42 TRYING [1]
% 7.64/1.42 TRYING [2]
% 7.64/1.42 TRYING [3]
% 7.64/1.43 TRYING [4]
% 7.64/1.45 TRYING [5]
% 8.17/1.51 TRYING [6]
% 9.21/1.66 TRYING [7]
% 12.40/2.11 TRYING [8]
% 36.53/5.55 TRYING [9]
% 41.52/6.27 TRYING [7]
% 44.05/6.60 TRYING [9]
% 50.96/7.68 % (7774)First to succeed.
% 52.00/7.73 % (7774)Refutation found. Thanks to Tanya!
% 52.00/7.73 % SZS status Theorem for Vampire---4
% 52.00/7.73 % SZS output start Proof for Vampire---4
% See solution above
% 52.00/7.77 % (7774)------------------------------
% 52.00/7.77 % (7774)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 52.00/7.77 % (7774)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 52.00/7.77 % (7774)Termination reason: Refutation
% 52.00/7.77
% 52.00/7.77 % (7774)Memory used [KB]: 81619
% 52.00/7.77 % (7774)Time elapsed: 7.403 s
% 52.00/7.77 % (7774)------------------------------
% 52.00/7.77 % (7774)------------------------------
% 52.00/7.77 % (7675)Success in time 7.466 s
% 52.00/7.77 % Vampire---4.8 exiting
%------------------------------------------------------------------------------